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Radical Functions

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

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Graph the function y=−34(x−2)+3y=-3\sqrt{4(x-2)}+3.
More Radical Functions Questions:
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Function composition
Consider the functions f(x)=x1/23−xf(x)=\frac{x^{1/2}}{\sqrt{3-\sqrt{x}}} and g(x)=(6−x)2g(x)=(6-x)^2. Find (f∘g)(x)(f\circ g)(x) and the domain.
Absolute Value Functions: Function Properties
If f(x)=∣x−2∣, g(x)=3−x+1f\left(x\right)=\left|x-2\right|,\ g\left(x\right)=3-\sqrt{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)?
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Radical Functions
State the domain and range of the function f(x)=1x2−4f\left(x\right)=\dfrac{1}{\sqrt{x^2-4}}.
Consider the functions f(x)=x25−x2f\left(x\right)=\dfrac{x^2}{\sqrt{5-x^2}} and g(x)=2−xg\left(x\right)=\sqrt{2-x}
a. Find (f∘g)(x)(f \circ g)(x)
b. Find the domain of (f∘g)(x)(f \circ g)(x) . Enter in interval notation.
Radical Functions
Find the domain of f(x)=1x2−4−3f\left(x\right)=\dfrac{1}{\sqrt{x^2-4}-3}
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Radical Functions
Solve for xx:
3x3−3x2+1=x^3\sqrt{x^{3}-3x^2}+1=x
Solving Radical Equations
Solve for a:
2a+4−3=3a−22\sqrt{a+4}-3=\sqrt{3a-2}
Solving Radical Equations
Solve for xx:
2x−1=x\sqrt{2x-1}=\sqrt{x}
Solving Radical Equations
Practice: Solving Radical Equations
Solve algebraically, stating any restrictions:
x−6+3=x+9\sqrt{x-6}+3=\sqrt{x+9}
Solving Radical Equations
Practice: Solving Radical Equations
Solve algebraically, stating any restrictions:
x2−2=x+4\sqrt{x^2-2}=\sqrt{x+4}
Solving Radical Equations
Practice: Solving Radical Equations
Solve algebraically, stating any restrictions on xx:
10+10x−1=13\begin{array}{rcl} 10+\sqrt{10x-1}&=&13 \end{array}
Solving Radical Equations
Practice: Solving Radical Equations
Solve algebraically, stating any restrictions on xx:
x−3=3x−4\begin{array}{rcl} x-3&=&3\sqrt{x-4} \end{array}
Transformations of Radical Functions
Practice: Transformations of Radical Functions
Which of the following is the graph of the function y=−−3x+6−2y=-\sqrt{-3x+6}-2?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
Which of the following is the graph of the function y=4x−1y=\sqrt{4x}-1?
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Absolute Value Functions: Function Properties
If f(x)=∣x−2∣, g(x)=3−x+1f\left(x\right)=\left|x-2\right|,\ g\left(x\right)=3-\sqrt{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)?
Domain & Range
Practice: Domain & Range
If f(x)=2−xf\left(x\right)=2-\sqrt{x} and g(x)=x2−9g\left(x\right)=x^2-9, find the domain and range of f(g(x))f\left(g\left(x\right)\right).
Consider the functions f(x)=x25−x2f\left(x\right)=\dfrac{x^2}{\sqrt{5-x^2}} and g(x)=2−xg\left(x\right)=\sqrt{2-x}
a. Find (f∘g)(x)(f \circ g)(x)
b. Find the domain of (f∘g)(x)(f \circ g)(x) . Enter in interval notation.
Radical Functions
Find the domain of f(x)=1x2−4−3f\left(x\right)=\dfrac{1}{\sqrt{x^2-4}-3}
Radical Functions
State the domain and range of the function f(x)=1x2−4f\left(x\right)=\dfrac{1}{\sqrt{x^2-4}}.
Function composition
Consider the functions f(x)=x1/23−xf(x)=\frac{x^{1/2}}{\sqrt{3-\sqrt{x}}} and g(x)=(6−x)2g(x)=(6-x)^2. Find (f∘g)(x)(f\circ g)(x) and the domain.
Radical Functions
Given the function g(x)=3+5+7xg\left(x\right)=3+\sqrt{5+7x}
Fill in the blanks using the following options:
{x : x<75},  {x : x≥75} ,  {x : x≤75} , {x : x>75} \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\}\
More Transformations of Radical Functions Questions:
Solving Radical Equations
Practice: Transformations
Let y=f(x)y=\sqrt{f(x)}.
Match the appropriate transformation with its transformed function.
Solving Radical Equations
Practice: Transformations
Let y=f(x)y=\sqrt{f(x)}.
Match the appropriate transformation with its transformed function.
Transformations of Radical Functions
Practice: Transformations of Radical Functions
If the point (-4,5) is on the function y=23f(−x−8)+13y=\frac{2}{3}f(-x-8)+\dfrac{1}{3}, then what point must be on the function y=f(x)y=\sqrt{f(x)}?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
If the point (2, 3) is on the function y=2f(x−1)−3y=2f(x-1)-3, then what point must be on the function y=f(x)y=\sqrt{f(x)}?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
Which of the following is the graph of the function y=−−3x+6−2y=-\sqrt{-3x+6}-2?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
Which of the following is the graph of the function y=4x−1y=\sqrt{4x}-1?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
If the point (x,64x52) (x,64x^{\frac{5}{2}})~ lies on the graph y=f(x),y=f(x), then what point lies on the graph y=f(x)y=\sqrt{f(x)}?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
If the point (x,81x16) (x,81x^{16})~ lies on the graph y=f(x),y=f(x), then what point lies on the graph y=f(x)y=\sqrt{f(x)}?
More Transformations of Radical Functions Questions:
Solving Radical Equations
Practice: Transformations
Let y=f(x)y=\sqrt{f(x)}.
Match the appropriate transformation with its transformed function.
Solving Radical Equations
Practice: Transformations
Let y=f(x)y=\sqrt{f(x)}.
Match the appropriate transformation with its transformed function.
Transformations of Radical Functions
Practice: Transformations of Radical Functions
If the point (-4,5) is on the function y=23f(−x−8)+13y=\frac{2}{3}f(-x-8)+\dfrac{1}{3}, then what point must be on the function y=f(x)y=\sqrt{f(x)}?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
If the point (2, 3) is on the function y=2f(x−1)−3y=2f(x-1)-3, then what point must be on the function y=f(x)y=\sqrt{f(x)}?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
Which of the following is the graph of the function y=−−3x+6−2y=-\sqrt{-3x+6}-2?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
Which of the following is the graph of the function y=4x−1y=\sqrt{4x}-1?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
If the point (x,64x52) (x,64x^{\frac{5}{2}})~ lies on the graph y=f(x),y=f(x), then what point lies on the graph y=f(x)y=\sqrt{f(x)}?
Transformations of Radical Functions
Practice: Transformations of Radical Functions
If the point (x,81x16) (x,81x^{16})~ lies on the graph y=f(x),y=f(x), then what point lies on the graph y=f(x)y=\sqrt{f(x)}?