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Absolute Value Functions: Function Properties
Related Topics
Wize University Calculus 1 Textbook > Pre-Calculus (Review)
Radical Functions
4 Activities
Wize University Calculus 1 Textbook > Pre-Calculus (Review)
Absolute Value Functions
2 Activities
If
f
(
x
)
=
∣
x
−
2
∣
,
g
(
x
)
=
3
−
x
+
1
f\left(x\right)=\left|x-2\right|,\ g\left(x\right)=3-\sqrt{x+1}
f
(
x
)
=
∣
x
−
2
∣
,
g
(
x
)
=
3
−
x
+
1
, which of the following is true about
h
(
x
)
=
g
(
f
(
x
)
)
h\left(x\right)=g\left(f\left(x\right)\right)
h
(
x
)
=
g
(
f
(
x
)
)
?
a. It is a monotonic function
b. It has a minimum value of 3
c. It's domain is
[
−
1
,
∞
)
\left[-1,\infty\right)
[
−
1
,
∞
)
d. It is not defined on all points in
(
−
∞
,
∞
)
\left(-\infty,\infty\right)
(
−
∞
,
∞
)
e. None of the above
I don't know
Check Submission
More Radical Functions Questions:
Domain & Range
Practice: Domain & Range
If
f
(
x
)
=
2
−
x
f\left(x\right)=2-\sqrt{x}
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
−
9
g\left(x\right)=x^2-9
g
(
x
)
=
x
2
−
9
, find the domain and range of
f
(
g
(
x
)
)
f\left(g\left(x\right)\right)
f
(
g
(
x
)
)
.
Function composition
Consider the functions
f
(
x
)
=
x
1
/
2
3
−
x
f(x)=\frac{x^{1/2}}{\sqrt{3-\sqrt{x}}}
f
(
x
)
=
3
−
x
x
1/2
and
g
(
x
)
=
(
6
−
x
)
2
g(x)=(6-x)^2
g
(
x
)
=
(
6
−
x
)
2
. Find
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
and the domain.
Domain & Range
Practice: Domain & Range
If
f
(
x
)
=
2
−
x
f\left(x\right)=2-\sqrt{x}
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
−
9
g\left(x\right)=x^2-9
g
(
x
)
=
x
2
−
9
, find the domain and range of
f
(
g
(
x
)
)
f\left(g\left(x\right)\right)
f
(
g
(
x
)
)
.
Radical Functions
State the domain and range of the function
f
(
x
)
=
1
x
2
−
4
f\left(x\right)=\dfrac{1}{\sqrt{x^2-4}}
f
(
x
)
=
x
2
−
4
1
.
Consider the functions
f
(
x
)
=
x
2
5
−
x
2
f\left(x\right)=\dfrac{x^2}{\sqrt{5-x^2}}
f
(
x
)
=
5
−
x
2
x
2
and
g
(
x
)
=
2
−
x
g\left(x\right)=\sqrt{2-x}
g
(
x
)
=
2
−
x
a. Find
(
f
∘
g
)
(
x
)
(f \circ g)(x)
(
f
∘
g
)
(
x
)
b. Find the domain of
(
f
∘
g
)
(
x
)
(f \circ g)(x)
(
f
∘
g
)
(
x
)
. Enter in interval notation.
Radical Functions
Find the domain of
f
(
x
)
=
1
x
2
−
4
−
3
f\left(x\right)=\dfrac{1}{\sqrt{x^2-4}-3}
f
(
x
)
=
x
2
−
4
−
3
1
Domain & Range
Practice: Domain & Range
If
f
(
x
)
=
2
−
x
f\left(x\right)=2-\sqrt{x}
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
−
9
g\left(x\right)=x^2-9
g
(
x
)
=
x
2
−
9
, find the domain and range of
f
(
g
(
x
)
)
f\left(g\left(x\right)\right)
f
(
g
(
x
)
)
.
Radical Functions
Solve for
x
x
x
:
3
x
3
−
3
x
2
+
1
=
x
^3\sqrt{x^{3}-3x^2}+1=x
3
x
3
−
3
x
2
+
1
=
x
Solving Radical Equations
Solve for a:
2
a
+
4
−
3
=
3
a
−
2
2\sqrt{a+4}-3=\sqrt{3a-2}
2
a
+
4
−
3
=
3
a
−
2
Solving Radical Equations
Solve for
x
x
x
:
2
x
−
1
=
x
\sqrt{2x-1}=\sqrt{x}
2
x
−
1
=
x
Radical Functions
Graph the function
y
=
−
3
4
(
x
−
2
)
+
3
y=-3\sqrt{4(x-2)}+3
y
=
−
3
4
(
x
−
2
)
+
3
.
Solving Radical Equations
Practice: Solving Radical Equations
Solve algebraically, stating any restrictions:
x
−
6
+
3
=
x
+
9
\sqrt{x-6}+3=\sqrt{x+9}
x
−
6
+
3
=
x
+
9
Solving Radical Equations
Practice: Solving Radical Equations
Solve algebraically, stating any restrictions:
x
2
−
2
=
x
+
4
\sqrt{x^2-2}=\sqrt{x+4}
x
2
−
2
=
x
+
4
Solving Radical Equations
Practice: Solving Radical Equations
Solve algebraically, stating any restrictions on
x
x
x
:
10
+
10
x
−
1
=
13
\begin{array}{rcl} 10+\sqrt{10x-1}&=&13 \end{array}
10
+
10
x
−
1
=
13
Solving Radical Equations
Practice: Solving Radical Equations
Solve algebraically, stating any restrictions on
x
x
x
:
x
−
3
=
3
x
−
4
\begin{array}{rcl} x-3&=&3\sqrt{x-4} \end{array}
x
−
3
=
3
x
−
4
Transformations of Radical Functions
Practice: Transformations of Radical Functions
Which of the following is the graph of the function
y
=
−
−
3
x
+
6
−
2
y=-\sqrt{-3x+6}-2
y
=
−
−
3
x
+
6
−
2
?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
Which of the following is the graph of the function
y
=
4
x
−
1
y=\sqrt{4x}-1
y
=
4
x
−
1
?
Domain & Range
Practice: Domain & Range
If
f
(
x
)
=
2
−
x
f\left(x\right)=2-\sqrt{x}
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
−
9
g\left(x\right)=x^2-9
g
(
x
)
=
x
2
−
9
, find the domain and range of
f
(
g
(
x
)
)
f\left(g\left(x\right)\right)
f
(
g
(
x
)
)
.
Domain & Range
Practice: Domain & Range
If
f
(
x
)
=
2
−
x
f\left(x\right)=2-\sqrt{x}
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
−
9
g\left(x\right)=x^2-9
g
(
x
)
=
x
2
−
9
, find the domain and range of
f
(
g
(
x
)
)
f\left(g\left(x\right)\right)
f
(
g
(
x
)
)
.
Absolute Value Functions: Function Properties
If
f
(
x
)
=
∣
x
−
2
∣
,
g
(
x
)
=
3
−
x
+
1
f\left(x\right)=\left|x-2\right|,\ g\left(x\right)=3-\sqrt{x+1}
f
(
x
)
=
∣
x
−
2
∣
,
g
(
x
)
=
3
−
x
+
1
, which of the following is true about
h
(
x
)
=
g
(
f
(
x
)
)
h\left(x\right)=g\left(f\left(x\right)\right)
h
(
x
)
=
g
(
f
(
x
)
)
?
Domain & Range
Practice: Domain & Range
If
f
(
x
)
=
2
−
x
f\left(x\right)=2-\sqrt{x}
f
(
x
)
=
2
−
x
and
g
(
x
)
=
x
2
−
9
g\left(x\right)=x^2-9
g
(
x
)
=
x
2
−
9
, find the domain and range of
f
(
g
(
x
)
)
f\left(g\left(x\right)\right)
f
(
g
(
x
)
)
.
Consider the functions
f
(
x
)
=
x
2
5
−
x
2
f\left(x\right)=\dfrac{x^2}{\sqrt{5-x^2}}
f
(
x
)
=
5
−
x
2
x
2
and
g
(
x
)
=
2
−
x
g\left(x\right)=\sqrt{2-x}
g
(
x
)
=
2
−
x
a. Find
(
f
∘
g
)
(
x
)
(f \circ g)(x)
(
f
∘
g
)
(
x
)
b. Find the domain of
(
f
∘
g
)
(
x
)
(f \circ g)(x)
(
f
∘
g
)
(
x
)
. Enter in interval notation.
Radical Functions
Find the domain of
f
(
x
)
=
1
x
2
−
4
−
3
f\left(x\right)=\dfrac{1}{\sqrt{x^2-4}-3}
f
(
x
)
=
x
2
−
4
−
3
1
Radical Functions
State the domain and range of the function
f
(
x
)
=
1
x
2
−
4
f\left(x\right)=\dfrac{1}{\sqrt{x^2-4}}
f
(
x
)
=
x
2
−
4
1
.
Function composition
Consider the functions
f
(
x
)
=
x
1
/
2
3
−
x
f(x)=\frac{x^{1/2}}{\sqrt{3-\sqrt{x}}}
f
(
x
)
=
3
−
x
x
1/2
and
g
(
x
)
=
(
6
−
x
)
2
g(x)=(6-x)^2
g
(
x
)
=
(
6
−
x
)
2
. Find
(
f
∘
g
)
(
x
)
(f\circ g)(x)
(
f
∘
g
)
(
x
)
and the domain.
Radical Functions
Given the function
g
(
x
)
=
3
+
5
+
7
x
g\left(x\right)=3+\sqrt{5+7x}
g
(
x
)
=
3
+
5
+
7
x
Fill in the blanks using the following options:
{
x
:
x
<
7
5
}
,
{
x
:
x
≥
7
5
}
,
{
x
:
x
≤
7
5
}
,
{
x
:
x
>
7
5
}
\left\{x\ :\ x<\frac{7}{5}\right\},\ \ \left\{x\ :\ x\ge\frac{7}{5}\right\}\ ,\ \ \left\{x\ :\ x\le\frac{7}{5}\right\}\ ,\ \left\{x\ :\ x>\frac{7}{5}\right\}\
{
x
:
x
<
5
7
}
,
{
x
:
x
≥
5
7
}
,
{
x
:
x
≤
5
7
}
,
{
x
:
x
>
5
7
}
More Absolute Value Functions Questions:
Solve the following inequality
∣
2
x
−
3
∣
+
∣
x
−
4
∣
≥
3
\left|2x-3\right|+\left|x-4\right|\ge3
∣
2
x
−
3
∣
+
∣
x
−
4
∣
≥
3
Absolute Value Functions: Inequalities with Absolute Values
Solve the following inequality:
∣
x
+
1
∣
≥
x
+
4
2
\displaystyle\left|x+1\right|\ge\frac{x+4}{2}
∣
x
+
1
∣
≥
2
x
+
4
Absolute Value Functions: Inequality with Absolute Values
Find all
x
x
x
that satisfy the inequality
∣
x
2
−
3
x
+
1
∣
<
1
\left|x^2−3x+1\right|<1
x
2
−
3
x
+
1
<
1
Absolute Value Functions: Function Properties
If
f
(
x
)
=
∣
x
−
2
∣
,
g
(
x
)
=
3
−
x
+
1
f\left(x\right)=\left|x-2\right|,\ g\left(x\right)=3-\sqrt{x+1}
f
(
x
)
=
∣
x
−
2
∣
,
g
(
x
)
=
3
−
x
+
1
, which of the following is true about
h
(
x
)
=
g
(
f
(
x
)
)
h\left(x\right)=g\left(f\left(x\right)\right)
h
(
x
)
=
g
(
f
(
x
)
)
?
Absolute Value Functions
Solve the inequality for
x
x
x
,
∣
3
x
−
4
∣
+
∣
x
−
2
∣
≥
5
|3x-4|+|x-2| \geq 5
∣3
x
−
4∣
+
∣
x
−
2∣
≥
5
.
Solve the following inequality
∣
2
x
−
3
∣
+
∣
x
−
4
∣
≥
3
\left|2x-3\right|+\left|x-4\right|\ge3
∣
2
x
−
3
∣
+
∣
x
−
4
∣
≥
3
Absolute Value Functions: Inequalities with Absolute Values
Solve the following inequality:
∣
x
+
1
∣
≥
x
+
4
2
\displaystyle\left|x+1\right|\ge\frac{x+4}{2}
∣
x
+
1
∣
≥
2
x
+
4
Absolute Value Functions: Inequality with Absolute Values
Find all
x
x
x
that satisfy the inequality
∣
x
2
−
3
x
+
1
∣
<
1
\left|x^2−3x+1\right|<1
x
2
−
3
x
+
1
<
1