Parent Function Transformations

Which of the parent functions have an asymptote? Choose all that apply.

• Quadratic

• Rational

• Logarithmic

• Square Root

• Exponential

Tags

CCSS.HSA.APR.D.7

CCSS.HSF.IF.B.4

CCSS.HSF.IF.C.7

The graph of $f\left(x\right)=\sqrt{x}$ is transformed to create  $g\left(x\right)=f\left(x+5\right)-1$ . Describe the graph of g(x) in relation to f(x). 

• shifted left 5 units

• shifted right 5 units

• shifted up 1 unit

• shifted down 1 unit

• reflection across the x-axis

Tags

CCSS.HSF.BF.B.3

Describe the transformations for the following function $h\left(x\right)=2\left(x-3\right)^2+5$ from the parent function  $g\left(x\right)=x^2$   

• vertical stretch times 2

• horizontal stretch times 2

• shift left 3 units

• shift up 5 units

• shift right 3 units

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

Describe the transformation of f(x) to g(x) from the graph.

• shift left 2 units

• shift right 2 units

• vertical stretch

• horizontal stretch

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

What are the domain and range of g(x)?

• D: [-2, infinity) R: (0, infinity)

• D: [-2, infinity) R: [0, infinity)

• D: [-2, infinity) R: [1, infinity)

• D: [-2, infinity) R: (1, infinity)

Which parent function does NOT have an x-intercept and y-intercept at the origin?

• $f\left(x\right)=\left|x\right|$

• $g\left(x\right)=\log_2x$

• $h\left(x\right)=\sqrt{x}$

• $k\left(x\right)=x^2$

The graph of $f\left(x\right)$ is transformed to create  $g\left(x\right)=3f\left(x\right)$ . Which of the following describes the transformation?

• f(x) is translated 3 units left

• f(x) is vertically stretched by a factor of 3

• f(x) translated 3 units up

• f(x)  is horizontally stretched by a factor of 3

Tags

CCSS.HSF.BF.B.3

Describe the transformations of the function $g\left(x\right)=-\left|x+2\right|-7$  from the parent function  $f\left(x\right)=\left|x\right|$  

• reflection across x axis

• reflection across y axis

• shift left 2

• shift right 2

• down 7

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2

CCSS.HSG.CO.A.5

Which of the following does not describe the graph of the parent function of a quadratic equation?

• The graph has a range of all real numbers

• The x-intercept is 0

• The y-intercept is 0

• The graph has a domain of all real numbers

Describe the transformation of $g\left(x\right)=\frac{1}{2}\left(x+4\right)^3$ from the parent function  $f\left(x\right)=x^3$ . 

• vertical compression times 1/2; shift right 4 units

• horizontal compression times 1/2; shift left 4 units

• vertical compression times 1/2; shift left 4 units

• horizontal stretch times 2; shift right 4 units

Tags

CCSS.HSF.BF.B.3

CCSS.HSG.CO.A.2