Unit 7 Quizizz Lesson #1

Base Equation for Transforming Exponential
Functions

The parent function will be:

Multiple Choice

What is the parent function of this exponential function?

$$g\left(x\right)=2\cdot3^x$$

• $$f\left(x\right)=3^x$$

• $$f\left(x\right)=2\cdot3^x$$

Multiple Choice

What is the parent function of this exponential function?

$$g\left(x\right)=\frac{1}{2}\cdot4^{\left(x-3\right)}+6$$

• $$f\left(x\right)=4^x$$

• $$f\left(x\right)=\frac{1}{2}\cdot4^x$$

Translating (Moving) Left/Right

“h”makes the function move

LEFT or RIGHT

If h is POSITIVE

(x + 4, x + 3, x + 12)

The function moves LEFT

If h is NEGATIVE
(x - 4, x - 3, x - 12)

The function moves RIGHT

Translating (Moving) Up/Down

“k”makes the function move

UP or DOWN

If k is POSITIVE

(3x + 6, 3x+ 3, 3x+ 12)
The function moves UP

If k is NEGATIVE

(3x - 4, 3x - 3, 3x - 12)

The function moves DOWN

Example #1

Describe the
transformation in the
following exponential
function.

Move Up 3

Example #2

Describe the
transformation in the
following exponential
function.

Move Right 5

Example #3

Describe the
transformation in the
following exponential
function.

Move Left 3
Move Down 4

Multiple Choice

What transformations occur in the following function?

• right 3, up 2
• left 3, up 2
• left 3, down 2
• right 3, down 2

Multiple Choice

If g(x) is a transformation of f(x), describe the transformation.

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

• Up 4 units

• Down 4 units

• Left 4 units

• Right 4 units

Multiple Choice

Describe the transformation: $$f\left(x\right)\ =\ 3^{\left(x-2\right)}+5$$  

• left 2 up 5

• right 2 up 5

• left 2 down 5

• right 2 down 5

Multiple Choice

For $$y=a\left(b\right)^x+k$$ , how does adding a constant "k" transform the parent function?

• Horizontal shift

• Vertical Translation

• Reflection over the x-axis

• Reflection over the y-axis

Vertical Dilation

“a”makes the function either

vertically COMPRESS or STRETCH

If a is a FRACTION
(½∙2x , ¾∙2x, ⅔∙2x)

The function

compresses vertically

If a is a WHOLE NUMBER

(2∙2x, 4∙2x, 5∙2x, 12∙2x)

The function

stretches vertically

Describe the
transformation in the
following exponential
function.

Example #1

Vertical Stretch

Describe the
transformation in the
following exponential
function.

Example #2

Vertical Compression

Describe the
transformation in the
following exponential
function.

Example #3

Vertical Stretch
Move Down 2

Multiple Choice

$$f\left(x\right)=3^x\ \ \ \ and\ \ \ g\left(x\right)=5\left(3\right)^x$$  
What transformation has taken place from the parent function to g(x)

• Vertical Stretch

• Vertical Compression

• Translation up 5 units

• Reflection across the x-axis

Multiple Choice

Describe the transformations of the exponential function shown.

• Shrink by a factor of 2/3 and shift right 10.

• Shrink by a factor of 2/3 and shift left 10.

• Stretch by a factor of 5 and shift left 10.

• Stretch by a factor of 5 and shift right 10.

Multiple Choice

Given the original exponential function defined by y=4^x, how would the graph change if the function were:

y=2(4)^x-3+1?

• Vertically stretched by a factor of 2, right 3, and up 1

• Vertically compressed by a factor of 1/2, left 3 and down 1

• Vertically compressed by a factor of 1/2, right 3, and down 1

• Vertically stretched by a factor of 2, left 3, and up 1

Reflections of Functions (over x-axis)

f(x) = -a(x - h)2 + k

When there is a NEGATIVE
sign in front (outside) of your
parentheses, the graph of the
function will REFLECT over the

x-axis.

Translations of Functions (up & down)

f(x) = a(x - h)2 + k

When k is POSITIVE (plus

sign), the graph of the
function translates UP.

When k is NEGATIVE (minus

sign), the graph of the

function translates DOWN.

Translations of Functions (left & right)

f(x) = a(x - h)2 + k

CAUTION: This transformation is
OPPOSITE of what you expect.

When h is POSITIVE (plus sign), the

function will translate LEFT.

When h is NEGATIVE (minus sign),

the function will translate RIGHT.

Multiple Choice

Describe the transformation of y = (x - 4)²

• Shift UP
• Shift DOWN
• Shift LEFT
• Shift RIGHT

Multiple Choice

Describe the transformation of y = x² + 4

• Shift UP
• Shift DOWN
• Shift LEFT
• Shift RIGHT

Multiple Choice

Compare the function y = 5x² to the parent function y = x²

• Wider
• Narrower

Multiple Choice

How did we transform from the parent function?
y = x² + 2

• horizontal shift up
• vertical shift up
• horizontal shift down
• vertical shift down

Multiple Choice

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

• g(x)=x²-5
• g(x)=x²+5
• g(x)=(x-5)²
• g(x)=(x+5)²

Dilations of Functions (stretch)

f(x)=a(x - h)2 + k

When a is a number BIGGER than 1,

the function graph will STRETCH,

getting more NARROW.

Dilations of Functions (compression)

f(x)=a(x - h)2 + k

When a is a number SMALLER than 1
(like a fraction between 0 and 1), the

function graph will COMPRESS,

getting more WIDE.

Multiple Choice

Compare the function y = 0.3x² to the parent function y = x²

• Wider
• Narrower

Multiple Choice

In the equation f(x)=5(x+3)²-10 what does the 5 do?

• Vertical stretch by 5
• Horizontal compress by 5
• Reflect
• Move up 5