Shifts, flips and stretches of the parent functions: root, reciprocal, exponential and logarithmic

Answer Key - Grade 11 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Milo's worksheet has (9, 3) on y = √x. The graph moves to g(x) = √(x − 2) + 3. Where does the point land?

   (11, 6)
2. 2.

   Pia shifts y = 1/x in pencil to g(x) = 1/(x − 4) + 2. Where does (1, 1) go?

   (5, 3)
3. 3.

   On a puzzle card, (-8, -2) is on y = ∛x. Ren moves it to g(x) = ∛(x + 1) − 3. Which point is on g?

   (-9, -5)
4. 4.

   Tala's worksheet has (8, 2) on y = ∛x. Where is that point on g(x) = -∛x?

   (8, -2)
5. 5.

   In a notebook, Zee moves (8, 3) from y = log₂x to g(x) = log₂(-x). Which point is on g?

   (-8, 3)
6. 6.

   Ari redraws y = 2ˣ in pencil as g(x) = -2ˣ. Where does (3, 8) go?

   (3, -8)
7. 7.

   On a puzzle card, (9, 3) is on y = √x. Bo needs its point on g(x) = √(-x). Which point is it?

   (-9, 3)
8. 8.

   On a worksheet, Esme squeezes y = √x sideways to make g(x) = √(3x). Where does (9, 3) go?

   (3, 3)
9. 9.

   Kira's worksheet shows the graph of g, a moved copy of y = 2ˣ. Which equation is g?

   • g(x) = 2ˣ + 3
   • g(x) = 2ˣ − 3
   • g(x) = 2^(x − 3)
10. 10.

    “the curve y = log₂x moved” In a notebook, Luz has the graph of g, made by moving y = log₂x. What is the equation of g?

    • g(x) = log₂(x − 4)
    • g(x) = log₂x + 4
    • g(x) = log₂(x + 4)