Transform Function Reflect Translate

Explain the transformation of the function from y=x²: y = (x + 14)²

• translated up 14

• translated down 14

• translated right 14

• translated left 14

Given f(x) = (x-3)² + 5. What transformations took place from the original function f(x)?

• Left 3 up 5

• Right 3 down 5

• Left 3 down 5

• Right 3 up 5

The original graph is f(x). The new graph has been moved up 3 and to the right 4. The new graph is:

• f(x + 3) - 4

• f(x - 4) + 3

• f(x + 4) + 3

• f(x + 3) + 4

Compared to the parent function, f(x) = x², which of the following is the equation of the function after a vertical shrink by a factor of 1/3?

• A

• B

• C

• D

Sara used a graphing calculator to graph the function f(x) = 3(x + 2)² - 1. She plans to graph g(x) by changing the value of a from 3 to 1/3. How will the graph of g(x) compare to the graph of f(x)?

• The range of g(x) will be the same as the range of f(x).

• The graphs of f(x) and g(x) will open in opposite directions.

• The graph of g(x) will be narrower than the graph of f(x).

• The graphs of f(x) and g(x) will have the same y-intercept.

How did g(x) transform the Parent Function?

• Shifted up 4

• Shifted down 4

• Shifted left 4

• Shifted right 4

Which rule would result in a translation of 2 units left and 3 units up?

• (x, y) → (2x, 3y)

• (x, y) → (x - 2, y + 3)

• (x, y) → (-x, -y)

• (x, y) → (x + 2, y - 3)

Tags

CCSS.HSG.CO.A.2

Describe the translations necessary to transform the graph of f(x) into that of g(x).

• Translate up 2 units

• Translate right 2 units

• Translate down 2 units

• Translate left 2 units

Answer explanation

Vertex of f(x): (0, 0)

Vertex of g(x): (- 2, - 2)

From (0, 0) to (-2, -2), we must translate/shift/move left 2 AND down 2 units.

f(x) = 2x + 5 was changed to g(x) = 4x + 10. What transformation occurred?

• 2f(x)

• f(2x)

• f(x + 6)

• f(2x + 6)