High School
SAT
SAT Elite 1500
SAT Tutoring
ACT
ACT Elite 33
ACT Tutoring
University
MCAT
MCAT Elite 515
Med-School Admissions
Pre-Med Tutoring
Pre-Med Plus
LSAT
LSAT Elite 170
LSAT Self-Paced
LSAT Tutoring
DAT
DAT Elite
DAT Tutoring
Log in
Get Started for Free
Transformations
Related Topics
Wize University Calculus 1 Textbook > Pre-Calculus (Review)
Transformations of Functions
3 Activities
Wize University Calculus 1 Textbook > Pre-Calculus (Review)
Exponential Functions
3 Activities
Which of the following is the equation of the function produced by vertically shifting the graph of
y
=
e
x
y=e^x
y
=
e
x
up 3 units and then vertically stretching it by a factor of 4?
f
(
x
)
=
4
e
x
+
3
f(x)=4e^x+3
f
(
x
)
=
4
e
x
+
3
f
(
x
)
=
1
4
e
x
+
3
f(x)=\frac{1}{4}e^x+3
f
(
x
)
=
4
1
e
x
+
3
f
(
x
)
=
1
4
e
x
+
12
f(x)=\frac{1}{4}e^x+12
f
(
x
)
=
4
1
e
x
+
12
f
(
x
)
=
4
e
x
−
3
f(x)=4e^{x-3}
f
(
x
)
=
4
e
x
−
3
f
(
x
)
=
4
e
x
+
12
f(x)=4e^x+12
f
(
x
)
=
4
e
x
+
12
I don't know
Check Submission
More Transformations of Functions Questions:
Transforming a Log
Given
f
(
x
)
=
log
3
(
2
x
+
4
)
f\left(x\right)=\log_3\left(2x+4\right)
f
(
x
)
=
lo
g
3
(
2
x
+
4
)
, state all the transformations and draw a rough sketch of the function. State the asymptotes, intercepts, domain and range.
Transforming an Exponential
Given
f
(
x
)
=
−
2
e
3
x
−
6
+
1
f\left(x\right)=-2e^{3x-6}+1
f
(
x
)
=
−
2
e
3
x
−
6
+
1
, state all the transformations and draw a rough sketch of the function. State the asymptotes, intercepts, domain and range.
Transformation of Exponential Function
Find the equation of the graph that results from applying the following transformations in order to
y
=
e
x
y=e^x
y
=
e
x
:
Shifting the graph 2 units down and 1 unit left
Reflecting along the
x
x
x
axis
Practice: Transforming a Trig Function
Graph the function:
y
=
3
sin
(
2
x
+
π
2
)
+
1
\displaystyle y=3\sin\left(2x+\frac{\pi}{2}\right)+1
y
=
3
sin
(
2
x
+
2
π
)
+
1
Transforming a Log
Given
f
(
x
)
=
log
3
(
2
x
+
4
)
f\left(x\right)=\log_3\left(2x+4\right)
f
(
x
)
=
lo
g
3
(
2
x
+
4
)
, state all the transformations and draw a rough sketch of the function. State the asymptotes, intercepts, domain and range.
Transforming an Exponential
Given
f
(
x
)
=
−
2
e
3
x
−
6
+
1
f\left(x\right)=-2e^{3x-6}+1
f
(
x
)
=
−
2
e
3
x
−
6
+
1
, state all the transformations and draw a rough sketch of the function. State the asymptotes, intercepts, domain and range.
Q
:
\bf{Q:}
Q
:
State the transformations that have been applied to
y
=
x
5
2
y=x^{\frac{5}{2}}
y
=
x
2
5
to get:
y
=
2
(
−
3
x
+
4
)
5
2
−
1
y=2\left(-3x+4\right)^{\frac{5}{2}}-1
y
=
2
(
−
3
x
+
4
)
2
5
−
1
Practice: Transformation of Exponential Function
Practice: Transformation of Exponential Function
Find the equation of the graph that results from applying the following transformations in order to
y
=
e
x
y=e^x
y
=
e
x
:
Shifting the graph 2 units down and 1 unit left
Practice: Transformation of Exponential Function
Practice: Transformation of Exponential Function
Find the equation of the graph that results from applying the following transformations in order to
y
=
e
x
y=e^x
y
=
e
x
:
Shifting the graph 2 units down and 1 unit left
Transformation of Exponential Function
Find the equation of the graph that results from applying the following transformations in order to
y
=
e
x
y=e^x
y
=
e
x
:
Shifting the graph 2 units down and 1 unit left
Reflecting along the
x
x
x
axis
Transforming a Log
Given
f
(
x
)
=
log
3
(
2
x
+
4
)
f\left(x\right)=\log_3\left(2x+4\right)
f
(
x
)
=
lo
g
3
(
2
x
+
4
)
, state all the transformations and draw a rough sketch of the function. State the asymptotes, intercepts, domain and range.
Transforming an Exponential
Given
f
(
x
)
=
−
2
e
3
x
−
6
+
1
f\left(x\right)=-2e^{3x-6}+1
f
(
x
)
=
−
2
e
3
x
−
6
+
1
, state all the transformations and draw a rough sketch of the function. State the asymptotes, intercepts, domain and range.
Q
:
\bf{Q:}
Q
:
State the transformations that have been applied to
y
=
x
5
2
y=x^{\frac{5}{2}}
y
=
x
2
5
to get:
y
=
2
(
−
3
x
+
4
)
5
2
−
1
y=2\left(-3x+4\right)^{\frac{5}{2}}-1
y
=
2
(
−
3
x
+
4
)
2
5
−
1
Practice: Transforming a Trig Function
Graph the function:
y
=
3
sin
(
2
x
+
π
2
)
+
1
\displaystyle y=3\sin\left(2x+\frac{\pi}{2}\right)+1
y
=
3
sin
(
2
x
+
2
π
)
+
1
More Exponential Functions Questions:
Transforming an Exponential
Given
f
(
x
)
=
−
2
e
3
x
−
6
+
1
f\left(x\right)=-2e^{3x-6}+1
f
(
x
)
=
−
2
e
3
x
−
6
+
1
, state all the transformations and draw a rough sketch of the function. State the asymptotes, intercepts, domain and range.
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Which of the following functions, if any, has an inverse?
i.
f
(
x
)
=
3
x
−
1
f\left(x\right)=3x-1
f
(
x
)
=
3
x
−
1
ii.
f
(
x
)
=
−
5
f\left(x\right)=-5
f
(
x
)
=
−
5
Exponential Functions
Solve for
x
x
x
in the equation
3
x
2
−
15
=
(
x
2
−
5
)
e
4
−
x
3x^2−15=(x^2−5)e^{4-x}
3
x
2
−
15
=
(
x
2
−
5
)
e
4
−
x
Exponential Functions
If
3
x
2
−
15
=
(
x
2
−
5
)
e
4
−
x
3x^2−15=(x^2−5)e^{4-x}
3
x
2
−
15
=
(
x
2
−
5
)
e
4
−
x
, find
x
x
x
Exponential Functions
Solve for
x
x
x
in the equation
3
x
2
−
15
=
(
x
2
−
5
)
e
4
−
x
3x^2−15=(x^2−5)e^{4-x}
3
x
2
−
15
=
(
x
2
−
5
)
e
4
−
x
Properties of Functions
Which of the following statements is/are true about the functions
f
(
x
)
=
0
f\left(x\right)=0
f
(
x
)
=
0
,
g
(
x
)
=
x
3
cos
x
g\left(x\right)=x^3\ \cos x
g
(
x
)
=
x
3
cos
x
, and
h
(
x
)
=
e
sin
x
h\left(x\right)=e^{\sin x}
h
(
x
)
=
e
s
i
n
x
?
i. Exactly two of the functions are even.
ii. Exactly two of the functions are odd.
Log & Exponential Function Properties
Which of the following functions is/are always increasing?
Properties of Exponential Functions
If
f
(
x
)
=
−
4
⋅
e
3
x
π
⋅
2
2
x
f\left(x\right)=\frac{-4\cdot e^{3x}}{\pi\cdot2^{2x}}
f
(
x
)
=
π
⋅
2
2
x
−
4
⋅
e
3
x
, which of the following statements is true?
Exponential Functions: Domain & Range
Find the domain and range of
f
(
x
)
=
2
−
9
x
−
8
f\left(x\right)=\sqrt{2^{-9x}-8}
f
(
x
)
=
2
−
9
x
−
8
.
Exponential Functions
Which of the following statements is/are true about the exponential function
f
(
x
)
=
C
4
x
+
b
f\left(x\right)=C4^x+b
f
(
x
)
=
C
4
x
+
b
whose graph passes through the points
(
1
,
1
)
\left(1,1\right)
(
1
,
1
)
and
(
1
2
,
2
)
\left(\frac{1}{2},2\right)
(
2
1
,
2
)
?
i.
f
(
x
)
=
2
(
4
x
)
−
1
f\left(x\right)=2\left(4^x\right)-1
f
(
x
)
=
2
(
4
x
)
−
1
ii. It has a horizontal asymptote at
y
=
−
1
y=-1
y
=
−
1
Transformation of Exponential Function
Find the equation of the graph that results from applying the following transformations in order to
y
=
e
x
y=e^x
y
=
e
x
:
Shifting the graph 2 units down and 1 unit left
Reflecting along the
x
x
x
axis
Practice: Exponents Equation
Q
:
\bf{Q:}
Q
:
Solve for
x
x
x
in
2
x
2
−
x
=
64
2^{x^2-x}=64
2
x
2
−
x
=
64
Exponential Functions
Find the domain of the function
f
(
x
)
=
1
(
e
x
−
1
)
(
x
+
1
)
+
1
2
−
x
2
f\left(x\right)=\dfrac{1}{\left(e^x-1\right)\left(x+1\right)}+\dfrac{1}{\sqrt{2-x^2}}
f
(
x
)
=
(
e
x
−
1
)
(
x
+
1
)
1
+
2
−
x
2
1
Exponential and Trigonometric Functions
Q
:
\bf{Q:}
Q
:
Find the domain of .
f
(
x
)
=
sin
(
3
x
)
e
4
x
−
1
−
tan
(
2
x
)
f\left(x\right)=\dfrac{\sin\left(3x\right)}{e^{4x-1}}-\tan\left(2x\right)
f
(
x
)
=
e
4
x
−
1
sin
(
3
x
)
−
tan
(
2
x
)
Exponential Functions: Inequalities with Exponents
Find all
x
x
x
that satisfy the inequality
e
x
>
e
−
x
e^x>e^{−x}
e
x
>
e
−
x
Transforming an Exponential
Given
f
(
x
)
=
−
2
e
3
x
−
6
+
1
f\left(x\right)=-2e^{3x-6}+1
f
(
x
)
=
−
2
e
3
x
−
6
+
1
, state all the transformations and draw a rough sketch of the function. State the asymptotes, intercepts, domain and range.
Exponential Functions
Solve for
x
x
x
in the equation
3
x
2
−
15
=
(
x
2
−
5
)
e
4
−
x
3x^2−15=(x^2−5)e^{4-x}
3
x
2
−
15
=
(
x
2
−
5
)
e
4
−
x
Solving Exponential Equations
Solve
5
(
1
128
)
2
x
+
5
=
10
(
32
)
x
+
1
5\Bigg(\dfrac{1}{128}\Bigg)^{2x+5}=10(32)^{x+1}
5
(
128
1
)
2
x
+
5
=
10
(
32
)
x
+
1
Simplifying Exponential Expressions
Simplify
(
72
a
b
(
2
a
+
b
)
3
2
a
−
3
b
)
\Bigg(\dfrac{72^{ab}(2^{a+b})}{3^{2a-3b}}\Bigg)
(
3
2
a
−
3
b
7
2
ab
(
2
a
+
b
)
)
Solving Exponential Equations
Solve
4
(
8
)
3
x
+
1
=
32
(
4
)
x
+
2
4(8)^{3x+1}=32(4)^{x+2}
4
(
8
)
3
x
+
1
=
32
(
4
)
x
+
2
Solving Exponential Equations
Practice: Solving Exponential Equations
Solve for x:
4
x
−
6
(
2
x
)
+
8
=
0
4^x-6(2^x)+8=0
4
x
−
6
(
2
x
)
+
8
=
0
Solving Exponential Equations
Practice: Solving Exponential Equations
Solve for x:
3
2
x
−
3
x
=
0
3^{2x}-3^x=0
3
2
x
−
3
x
=
0
Solving Exponential Equations
Practice: Solving Exponential Equations
What value of
x
x
x
makes the following statement true? Leave answer in exact form.
(
216
125
)
3
x
=
(
36
25
)
2
x
−
1
\Bigg(\dfrac{216}{125}\Bigg)^{3x}=\Bigg(\dfrac{36}{25}\Bigg)^{2x-1}
(
125
216
)
3
x
=
(
25
36
)
2
x
−
1
Solving Exponential Equations
Practice: Solving Exponential Equations
What value of
x
x
x
makes the following statement true? Leave answer in exact form.
(
3
4
)
2
x
−
1
=
(
81
256
)
x
+
2
\Bigg(\dfrac{3}{4}\Bigg)^{2x-1}=\Bigg(\dfrac{81}{256}\Bigg)^{x+2}
(
4
3
)
2
x
−
1
=
(
256
81
)
x
+
2
Solving Exponential Equations
Practice: Solving Exponential Equations
Solve for x:
25
4
x
+
5
=
125
x
−
3
25^{4x+5}=125^{x-3}
2
5
4
x
+
5
=
12
5
x
−
3
. Leave answer as a fraction.
Solving Exponential Equations
Practice: Solving Exponential Equations
Solve for x:
4
2
x
+
1
=
8
3
x
−
1
4^{2x+1}=8^{3x-1}
4
2
x
+
1
=
8
3
x
−
1
. Leave answer as a fraction.
Exponential, Logarithmic and Trigonometric Functions
Which of the following numbers is the largest?
Practice: Transformation of Exponential Function
Practice: Transformation of Exponential Function
Find the equation of the graph that results from applying the following transformations in order to
y
=
e
x
y=e^x
y
=
e
x
:
Shifting the graph 2 units down and 1 unit left
Practice: Transformation of Exponential Function
Practice: Transformation of Exponential Function
Find the equation of the graph that results from applying the following transformations in order to
y
=
e
x
y=e^x
y
=
e
x
:
Shifting the graph 2 units down and 1 unit left
Log & Exponential Function Properties
Which of the following functions is/are always increasing?
Exponential Functions: Domain & Range
Find the domain and range of
f
(
x
)
=
2
−
9
x
−
8
f\left(x\right)=\sqrt{2^{-9x}-8}
f
(
x
)
=
2
−
9
x
−
8
.
Properties of Functions
Which of the following statements is/are true about the functions
f
(
x
)
=
0
f\left(x\right)=0
f
(
x
)
=
0
,
g
(
x
)
=
x
3
cos
x
g\left(x\right)=x^3\ \cos x
g
(
x
)
=
x
3
cos
x
, and
h
(
x
)
=
e
sin
x
h\left(x\right)=e^{\sin x}
h
(
x
)
=
e
s
i
n
x
?
i. Exactly two of the functions are even.
ii. Exactly two of the functions are odd.
Exponential Functions
Find the domain of the function
f
(
x
)
=
e
2
x
−
8
f\left(x\right)=e^{\sqrt{2x-8}}
f
(
x
)
=
e
2
x
−
8
Q
:
\bf{Q:}
Q
:
The lifespan of a mammal species is related to its heart rate by the function
L
(
h
)
=
120
h
−
0.01
L\left(h\right)=120h^{-0.01}
L
(
h
)
=
120
h
−
0.01
where
L
L
L
is the lifespan in years and
h
h
h
is the heart rate in beats per minute. Which of the following observations are true? Select all that apply.
Note: This question is for practice purposes only, it is not based on real scientific data.
Which of this functions represents a quantity that doubles every
3
3
3
years?
Practice: Solving Exponential Equations
Find all solutions to the equation
4
2
x
⋅
8
x
2
+
x
=
1
4
4^{2x}\cdot8^{x^2+x}=\frac{1}{4}
4
2
x
⋅
8
x
2
+
x
=
4
1
.
Transforming an Exponential
Given
f
(
x
)
=
−
2
e
3
x
−
6
+
1
f\left(x\right)=-2e^{3x-6}+1
f
(
x
)
=
−
2
e
3
x
−
6
+
1
, state all the transformations and draw a rough sketch of the function. State the asymptotes, intercepts, domain and range.
Exponential Functions
Solve for
x
x
x
in the equation
3
x
2
−
15
=
(
x
2
−
5
)
e
4
−
x
3x^2−15=(x^2−5)e^{4-x}
3
x
2
−
15
=
(
x
2
−
5
)
e
4
−
x
Exponential Functions: Inequalities with Exponents
Find all
x
x
x
that satisfy the inequality
e
x
>
e
−
x
e^x>e^{−x}
e
x
>
e
−
x
Exponential and Trigonometric Functions
Q
:
\bf{Q:}
Q
:
Find the domain of .
f
(
x
)
=
sin
(
3
x
)
e
4
x
−
1
−
tan
(
2
x
)
f\left(x\right)=\dfrac{\sin\left(3x\right)}{e^{4x-1}}-\tan\left(2x\right)
f
(
x
)
=
e
4
x
−
1
sin
(
3
x
)
−
tan
(
2
x
)
Exponential Functions
Find the domain of the function
f
(
x
)
=
1
(
e
x
−
1
)
(
x
+
1
)
+
1
2
−
x
2
f\left(x\right)=\dfrac{1}{\left(e^x-1\right)\left(x+1\right)}+\dfrac{1}{\sqrt{2-x^2}}
f
(
x
)
=
(
e
x
−
1
)
(
x
+
1
)
1
+
2
−
x
2
1
Practice: Exponents Equation
Q
:
\bf{Q:}
Q
:
Solve for
x
x
x
in
2
x
2
−
x
=
64
2^{x^2-x}=64
2
x
2
−
x
=
64
Practice: Exponential function
The exponential function
y
=
b
x
+
k
,
(
b
>
0
)
y=b^x+k,\ \left(b>0\right)
y
=
b
x
+
k
,
(
b
>
0
)
passes through the point
(
2
,
13
16
)
\left(2,\frac{13}{16}\right)
(
2
,
16
13
)
and has a horizontal asymptote at
y
=
1
4
y=\frac{1}{4}
y
=
4
1
.
Find the equation of this graph.
Exponential Functions
Solve the equation for
x
x
x
.
e
2
x
=
11
e
x
−
30
e^{2x}=11e^x-30
e
2
x
=
11
e
x
−
30
Exponential Functions
If
h
(
x
)
=
e
x
+
2
x
+
1
h\left(x\right)=e^x+2x+1
h
(
x
)
=
e
x
+
2
x
+
1
, find the value of
h
−
1
(
2
)
h^{-1}\left(2\right)
h
−
1
(
2
)
Exponential Functions
Find the domain of the function
f
(
x
)
=
1
8
−
2
−
3
x
f\left(x\right)=\frac{1}{\sqrt{8-2^{-3x}}}
f
(
x
)
=
8
−
2
−
3
x
1
Practice: Log & Exponential Function Properties
Practice: Log & Exponential Function Properties
Which of the following functions is/are always increasing?
Exponential Functions
The exponential function
y
=
b
x
+
k
,
(
b
>
0
)
y=b^x+k,\ \left(b>0\right)
y
=
b
x
+
k
,
(
b
>
0
)
passes through the point
(
2
,
13
16
)
\left(2,\frac{13}{16}\right)
(
2
,
16
13
)
and has a horizontal asymptote at
y
=
1
4
y=\frac{1}{4}
y
=
4
1
.
Find the equation of this graph.
Which of the following functions, if any, has an inverse?
i.
f
(
x
)
=
3
x
−
1
f\left(x\right)=3x-1
f
(
x
)
=
3
x
−
1
ii.
f
(
x
)
=
−
5
f\left(x\right)=-5
f
(
x
)
=
−
5
Exponential Functions
Find the domain of the function
f
(
x
)
=
1
8
−
2
−
3
x
f\left(x\right)=\frac{1}{\sqrt{8-2^{-3x}}}
f
(
x
)
=
8
−
2
−
3
x
1
Properties of Exponential Functions
If
f
(
x
)
=
−
4
⋅
e
3
x
π
⋅
2
2
x
f\left(x\right)=\frac{-4\cdot e^{3x}}{\pi\cdot2^{2x}}
f
(
x
)
=
π
⋅
2
2
x
−
4
⋅
e
3
x
, which of the following statements is true?
Exponential Functions
Which of the following statements is/are true about the exponential function
f
(
x
)
=
C
4
x
+
b
f\left(x\right)=C4^x+b
f
(
x
)
=
C
4
x
+
b
whose graph passes through the points
(
1
,
1
)
\left(1,1\right)
(
1
,
1
)
and
(
1
2
,
2
)
\left(\frac{1}{2},2\right)
(
2
1
,
2
)
?
i.
f
(
x
)
=
2
(
4
x
)
−
1
f\left(x\right)=2\left(4^x\right)-1
f
(
x
)
=
2
(
4
x
)
−
1
ii. It has a horizontal asymptote at
y
=
−
1
y=-1
y
=
−
1
Transformation of Exponential Function
Find the equation of the graph that results from applying the following transformations in order to
y
=
e
x
y=e^x
y
=
e
x
:
Shifting the graph 2 units down and 1 unit left
Reflecting along the
x
x
x
axis