Transformations of Functions

Describe the Transformation

100

f(x) = x² + 8

What is translation up 8.

200

f(x) = lx - 4l

What is translates to the right 4

300

f(x) = 1/2x³ - 5

What is Compression by 1/2 and down 5.

400

f(x) = -(x + 9) - 2

What is reflection across x-axis, translates left 9 and down 2.

500

f(x) = -3lx - 5l - 6

What is reflection across x-axis, stretch by a factor of 3, translates right 5 and down 6

Write the Function

100

The quadratic function translated down 3

What is g(x) = x² - 3

200

The absolute value function translated to the left 7

What is f(x) = lx + 7l

300

The cubic function reflected across the x-axis and translated down 5

What is h(x) = -x^3 - 5

400

The square root function translated right 8 and down 10

What is f(x) = sqrt(x - 8) - 10

500

The absolute value function reflected, horizontal shrink by 2, left 3, and up 4

What is g(x) = -2lx + 3l + 4

Domain and Range

100

f(x) = x² - 5

D:(-infinity, infinity) R: [-5, infinity)

200

h(x) = sqrt(x + 2)

D: [-2, infinity) R: [0, infinity)

300

g(x) = |x - 1|

D: (-infinity, infinity) R: [0, infinity)

400

f(x) = (x + 2)³ - 6

D: (-infinity, infinity) R: (-infinity, infinity)

500

g(x) = -(x - 5)² + 7

D: (-infinity, infinity) R: [7, -infinity)

Even/Odd

100

f(x)=4x+5

Odd

200

f(x)=x² - x + 20

Neither

300

f(x) = x⁶ - x⁴ + x² - 12

Even

400

f(x) = 7x³ + 2x² -11x + 1

Neither

500

Odd functions are symmetric over _____________.

Even functions are symmetric over ______________.

The origin.

The y-axis.

Average Rate of Change

100

What is the formula to find the average rate of change?

f(x₂)-f(x₁)/x₂-x₁

200

Calculate the average rate of change of f(x) = 2x+5 from x=0 to x=2

2

300

Find the average rate of change on the interval [1,2] for f(x)=x²-8

3

400

Calculate the average rate of change f(x)=-1x²+2x-3 on the interval [2,3]

-3

500

Find the average rate of change for f(x)=-3(x+2)²-10 from [-1,1]

-2