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Practice: Transformation of Exponential Function

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Wize University Calculus 1 Textbook > Pre-Calculus (Review)

Exponential Functions

3 Activities

Wize University Calculus 1 Textbook > Pre-Calculus (Review)

Transformations of Functions

3 Activities

Practice: Transformation of Exponential Function

Find the equation of the graph that results from applying the following transformations in order to y=exy=e^x:
  1. Shifting the graph 2 units down and 1 unit left
  2. Reflecting along the xx axis
  3. Stretching the graph vertically by a factor of 3
  4. Shifting the graph 1 unit down
  5. Reflecting along the xx axis
More Exponential Functions Questions:
Transforming an Exponential
Given f(x)=−2e3x−6+1f\left(x\right)=-2e^{3x-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 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Which of the following functions, if any, has an inverse?
i. f(x)=3x−1f\left(x\right)=3x-1
ii. f(x)=−5f\left(x\right)=-5
Exponential Functions
Solve for xx in the equation 3x2−15=(x2−5)e4−x3x^2−15=(x^2−5)e^{4-x}
Exponential Functions
If 3x2−15=(x2−5)e4−x3x^2−15=(x^2−5)e^{4-x}, find xx
Exponential Functions
Solve for xx in the equation 3x2−15=(x2−5)e4−x3x^2−15=(x^2−5)e^{4-x}
Properties of Functions
Which of the following statements is/are true about the functions f(x)=0f\left(x\right)=0, g(x)=x3 cos⁡xg\left(x\right)=x^3\ \cos x, and h(x)=esin⁡xh\left(x\right)=e^{\sin 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⋅e3xπ⋅22xf\left(x\right)=\frac{-4\cdot e^{3x}}{\pi\cdot2^{2x}}, which of the following statements is true?
Exponential Functions: Domain & Range
Find the domain and range of f(x)=2−9x−8f\left(x\right)=\sqrt{2^{-9x}-8}.
Exponential Functions
Which of the following statements is/are true about the exponential function f(x)=C4x+bf\left(x\right)=C4^x+b whose graph passes through the points (1,1)\left(1,1\right)and (12,2)\left(\frac{1}{2},2\right)?
i. f(x)=2(4x)−1f\left(x\right)=2\left(4^x\right)-1
ii. It has a horizontal asymptote at y=−1y=-1
Transformation of Exponential Function
Find the equation of the graph that results from applying the following transformations in order to y=exy=e^x:
Shifting the graph 2 units down and 1 unit left
Reflecting along the xx axis
Practice: Exponents Equation
Q:\bf{Q:} Solve for xx in 2x2−x=642^{x^2-x}=64
Exponential Functions
Find the domain of the function f(x)=1(ex−1)(x+1)+12−x2f\left(x\right)=\dfrac{1}{\left(e^x-1\right)\left(x+1\right)}+\dfrac{1}{\sqrt{2-x^2}}
Exponential and Trigonometric Functions
Q:\bf{Q:} Find the domain of . f(x)=sin⁡(3x)e4x−1−tan⁡(2x)f\left(x\right)=\dfrac{\sin\left(3x\right)}{e^{4x-1}}-\tan\left(2x\right)
Exponential Functions: Inequalities with Exponents
Find all xx that satisfy the inequality ex>e−xe^x>e^{−x}
Transforming an Exponential
Given f(x)=−2e3x−6+1f\left(x\right)=-2e^{3x-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 xx in the equation 3x2−15=(x2−5)e4−x3x^2−15=(x^2−5)e^{4-x}
Solving Exponential Equations
Solve 5(1128)2x+5=10(32)x+15\Bigg(\dfrac{1}{128}\Bigg)^{2x+5}=10(32)^{x+1}
Simplifying Exponential Expressions
Simplify (72ab(2a+b)32a−3b)\Bigg(\dfrac{72^{ab}(2^{a+b})}{3^{2a-3b}}\Bigg)
Solving Exponential Equations
Solve 4(8)3x+1=32(4)x+24(8)^{3x+1}=32(4)^{x+2}
Solving Exponential Equations
Practice: Solving Exponential Equations
Solve for x: 4x−6(2x)+8=04^x-6(2^x)+8=0
Solving Exponential Equations
Practice: Solving Exponential Equations
Solve for x: 32x−3x=03^{2x}-3^x=0
Solving Exponential Equations
Practice: Solving Exponential Equations
What value of xx makes the following statement true? Leave answer in exact form.
(216125)3x=(3625)2x−1\Bigg(\dfrac{216}{125}\Bigg)^{3x}=\Bigg(\dfrac{36}{25}\Bigg)^{2x-1}
Solving Exponential Equations
Practice: Solving Exponential Equations
What value of xx makes the following statement true? Leave answer in exact form.
(34)2x−1=(81256)x+2\Bigg(\dfrac{3}{4}\Bigg)^{2x-1}=\Bigg(\dfrac{81}{256}\Bigg)^{x+2}
Solving Exponential Equations
Practice: Solving Exponential Equations
Solve for x: 254x+5=125x−325^{4x+5}=125^{x-3}. Leave answer as a fraction.
Solving Exponential Equations
Practice: Solving Exponential Equations
Solve for x: 42x+1=83x−14^{2x+1}=8^{3x-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=exy=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)=2−9x−8f\left(x\right)=\sqrt{2^{-9x}-8}.
Properties of Functions
Which of the following statements is/are true about the functions f(x)=0f\left(x\right)=0, g(x)=x3 cos⁡xg\left(x\right)=x^3\ \cos x, and h(x)=esin⁡xh\left(x\right)=e^{\sin 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)=e2x−8f\left(x\right)=e^{\sqrt{2x-8}}
Transformations
Which of the following is the equation of the function produced by vertically shifting the graph of y=exy=e^x up 3 units and then vertically stretching it by a factor of 4?
Q:\bf{Q:} The lifespan of a mammal species is related to its heart rate by the function L(h)=120h−0.01L\left(h\right)=120h^{-0.01} where LL is the lifespan in years and hh 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 33 years?
Practice: Solving Exponential Equations
Find all solutions to the equation 42x⋅8x2+x=144^{2x}\cdot8^{x^2+x}=\frac{1}{4}.
Transforming an Exponential
Given f(x)=−2e3x−6+1f\left(x\right)=-2e^{3x-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 xx in the equation 3x2−15=(x2−5)e4−x3x^2−15=(x^2−5)e^{4-x}
Exponential Functions: Inequalities with Exponents
Find all xx that satisfy the inequality ex>e−xe^x>e^{−x}
Exponential and Trigonometric Functions
Q:\bf{Q:} Find the domain of . f(x)=sin⁡(3x)e4x−1−tan⁡(2x)f\left(x\right)=\dfrac{\sin\left(3x\right)}{e^{4x-1}}-\tan\left(2x\right)
Exponential Functions
Find the domain of the function f(x)=1(ex−1)(x+1)+12−x2f\left(x\right)=\dfrac{1}{\left(e^x-1\right)\left(x+1\right)}+\dfrac{1}{\sqrt{2-x^2}}
Practice: Exponents Equation
Q:\bf{Q:} Solve for xx in 2x2−x=642^{x^2-x}=64
Practice: Exponential function
The exponential function y=bx+k, (b>0)y=b^x+k,\ \left(b>0\right) passes through the point (2,1316)\left(2,\frac{13}{16}\right) and has a horizontal asymptote at y=14y=\frac{1}{4}.
Find the equation of this graph.
Exponential Functions
Solve the equation for xx .
e2x=11ex−30e^{2x}=11e^x-30
Exponential Functions
If h(x)=ex+2x+1h\left(x\right)=e^x+2x+1, find the value of h−1(2)h^{-1}\left(2\right)
Exponential Functions
Find the domain of the function f(x)=18−2−3xf\left(x\right)=\frac{1}{\sqrt{8-2^{-3x}}}
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=bx+k, (b>0)y=b^x+k,\ \left(b>0\right) passes through the point (2,1316)\left(2,\frac{13}{16}\right) and has a horizontal asymptote at y=14y=\frac{1}{4}.
Find the equation of this graph.
Which of the following functions, if any, has an inverse?
i. f(x)=3x−1f\left(x\right)=3x-1
ii. f(x)=−5f\left(x\right)=-5
Exponential Functions
Find the domain of the function f(x)=18−2−3xf\left(x\right)=\frac{1}{\sqrt{8-2^{-3x}}}
Properties of Exponential Functions
If f(x)=−4⋅e3xπ⋅22xf\left(x\right)=\frac{-4\cdot e^{3x}}{\pi\cdot2^{2x}}, which of the following statements is true?
Exponential Functions
Which of the following statements is/are true about the exponential function f(x)=C4x+bf\left(x\right)=C4^x+b whose graph passes through the points (1,1)\left(1,1\right)and (12,2)\left(\frac{1}{2},2\right)?
i. f(x)=2(4x)−1f\left(x\right)=2\left(4^x\right)-1
ii. It has a horizontal asymptote at y=−1y=-1
Transformation of Exponential Function
Find the equation of the graph that results from applying the following transformations in order to y=exy=e^x:
Shifting the graph 2 units down and 1 unit left
Reflecting along the xx axis
More Transformations of Functions Questions:
Transforming a Log
Given f(x)=log⁡3(2x+4)f\left(x\right)=\log_3\left(2x+4\right) , 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)=−2e3x−6+1f\left(x\right)=-2e^{3x-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=exy=e^x:
Shifting the graph 2 units down and 1 unit left
Reflecting along the xx axis
Practice: Transforming a Trig Function
Graph the function: y=3sin⁡(2x+π2)+1\displaystyle y=3\sin\left(2x+\frac{\pi}{2}\right)+1
Transforming a Log
Given f(x)=log⁡3(2x+4)f\left(x\right)=\log_3\left(2x+4\right) , 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)=−2e3x−6+1f\left(x\right)=-2e^{3x-6}+1 , state all the transformations and draw a rough sketch of the function. State the asymptotes, intercepts, domain and range.
Q:\bf{Q:} State the transformations that have been applied to y=x52y=x^{\frac{5}{2}} to get: y=2(−3x+4)52−1y=2\left(-3x+4\right)^{\frac{5}{2}}-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=exy=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=exy=e^x:
Shifting the graph 2 units down and 1 unit left
Reflecting along the xx axis
Transformations
Which of the following is the equation of the function produced by vertically shifting the graph of y=exy=e^x up 3 units and then vertically stretching it by a factor of 4?
Transforming a Log
Given f(x)=log⁡3(2x+4)f\left(x\right)=\log_3\left(2x+4\right) , 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)=−2e3x−6+1f\left(x\right)=-2e^{3x-6}+1 , state all the transformations and draw a rough sketch of the function. State the asymptotes, intercepts, domain and range.
Q:\bf{Q:} State the transformations that have been applied to y=x52y=x^{\frac{5}{2}} to get: y=2(−3x+4)52−1y=2\left(-3x+4\right)^{\frac{5}{2}}-1
Practice: Transforming a Trig Function
Graph the function: y=3sin⁡(2x+π2)+1\displaystyle y=3\sin\left(2x+\frac{\pi}{2}\right)+1