Quiz about Transformations on Parent Functions

Question 1

Write the equation that results if the parent absolute value function is shifted right 15 units, down 3 units, and reflected vertically.

Accepted Answer

$$y=-\left|x-15\right|-3$$

Answer

$$y=-\left|x+15\right|-3$$

Answer

$$y=\frac{1}{2}\left|x+3\right|-15$$

Answer

$$y=\frac{1}{2}\left|x-3\right|-15$$

Answer

$$y=\left|-x-15\right|-3$$

Question 2

Which transformations are involved in the equation $$y=\frac{1}{2}\sqrt{x+1}-1$$ ?

Accepted Answer

Vertical shrink

Accepted Answer

Horizontal translation left

Accepted Answer

Vertical translation down

Answer

Horizontal translation right

Answer

Vertical stretch

Question 3

If $$f\left(x\right)=a\left(x-h\right)^2+k$$ has a horiz. shift of -2, a vertical shift of +3 and a vertical stretch of 4, what are the values of a, h, and k?

Accepted Answer

$$a=4;\ h=-2;\ k=3$$

Answer

$$a=2;\ h=4;\ k=-3$$

Answer

$$a=4;\ h=2;\ k=3$$

Answer

$$a=3;\ h=2;\ k=-4$$

Question 4

If $$f\left(x\right)=a\left(x-h\right)^2+k$$ has a horiz. shift of -2, a vert. shift of 3 and a vert. stretch of 4, what is the equation for $$f\left(x\right)$$ ?

Accepted Answer

$$f\left(x\right)=4\left(x+2\right)^2+3$$

Answer

$$f\left(x\right)=4\left(x-2\right)^2+3$$

Answer

$$f\left(x\right)=3\left(x+2\right)^2+4$$

Answer

$$f\left(x\right)=2\left(x-4\right)^2+3$$

Question 5

Use the graphs of f and g to describe the transformation from the graph of f to the graph of g.

Accepted Answer

The graph of g is a horizontal translation of the graph of f, 4 units left

Answer

The graph of g is a vertical translation 4 units up from the graph f

Answer

The graph of g is a horizontal translation of the graph of f, 4 units right

Answer

The graph of g is a vertical stretch of the graph of f, by a factor of 7

Question 6

What does the transformationdo to the graph of $$f\left(x\right)$$ ?

Accepted Answer

translates it left one unit and down 9 units

Answer

translates it right one unit and down 9 units

Answer

translates it up one unit and right 9 units

Answer

translates it down one unit and left 9 units

Question 7

What does the transformationdo to the graph of ?

Accepted Answer

Shrinks the graph vertically by a factor of 1/3 and translates up 4 units.

Answer

Stretches the graph by a factor of 3 and translates up 4 units.

Answer

Translates the graph left 1/3 of a unit and up 4 units.

Answer

Translates the graph right 3 unites and down 4 units.

Question 8

Describe the transformations that would occur on the given function

Accepted Answer

horizontal shift to the right 4 and vertical shift down 2

Answer

horizontal shift to the left 4 and vertical shift down 2

Answer

horizontal shift to the right 4 and vertical shift up 2

Answer

horizontal shift to the left 4 and vertical shift up 2

Question 9

Question 9.

Accepted Answer

horizontal shift to the right 2 and vertical stretch by a factor of 3

Answer

horizontal shift to the left 2 and vertical stretch by a factor of 3

Answer

horizontal shift to the right 2 and vertical compression by a factor of 3

Answer

horizontal shift to the left 2 and vertical compression by a factor of 3

Question 10

If the blue is f(x)=x^2,then the red must be

Accepted Answer

g(x)=x2-5

Answer

g(x)=x2+5

Answer

g(x)=(x-5)²

Answer

g(x)=(x+5)²

Question 11

Name the parent function.

Accepted Answer

quadratic

Answer

linear

Answer

cubic

Answer

logarithmic

Question 12

Which equation below is a quadratic function translated left 4 units?

Accepted Answer

y = (x + 4)²

Answer

y = x² + 4

Answer

y = (x - 4)²

Answer

y = 4x2

Question 13

Tell how the graph transformed.
y = (x - 3)²

Accepted Answer

Translated right 3

Answer

Translated left 3

Answer

Translated up 3

Answer

Translated down 9

Question 14

Tell how the function transformed from y =x²
y = -2x²

Accepted Answer

Stretched vertically and reflected over x-axis

Answer

Translated left 2 units

Answer

Reflected over x-axis

Answer

Compressed vertically and reflected over the x-axis

Transformations on Parent Functions

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