Grade 11 · Math · Algebra 2

11th grade Shifts, flips and stretches of the parent functions: root, reciprocal, exponential and logarithmic worksheet

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

Grade 11 Math Worksheet - Challenge Me

NameDate

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

On a worksheet, f(x) = √x and g(x) = c√x. Pia reads g(9) = 15 from the graph of g. What is c?
In a notebook, Ren has f(x) = 2ˣ and g(x) = 2^(x − c), with g(7) = 8. What is c?
Tala works in pencil: g(x) = c/x is made from f(x) = 1/x, and g(4) = 5. What is c?
In a notebook, Bo has g(x) = ∛(x − 2) + 4 and wants the input with output 7. What is x?
Esme works in pencil: g(x) = 3√x − 5 and g(x) = 7. What is x?
On a puzzle card, g(x) = 2∛x + 1. Jun needs the x where g(x) = 7. What is x?
Kira's worksheet has (4, 2) on y = √x. Where is that point on g(x) = -2√(x − 1) + 3?
In a notebook, Luz moves (1, 2) from y = 2ˣ onto g(x) = 3 · 2^(x + 2) − 4. Which point is on g?
Milo redraws y = 1/x in pencil as g(x) = 4/(x − 3) + 1. Where does (2, 1/2) go?
On a puzzle card, (4, 2) is on y = log₂x. Noah needs its point on g(x) = -log₂(x + 5) + 2. Which point is it?

11th grade Shifts, flips and stretches of the parent functions: root, reciprocal, exponential and logarithmic worksheet – printable — Print: 1 2 3 4 5 6

About this worksheet

Shifts, flips and stretches of the parent functions: root, reciprocal, exponential and logarithmic. Every version has 10 questions, and the answer key prints on the second page.

What your child will learn

I can move a point of a parent graph to its place on the shifted, flipped or stretched graph.
I can name a stretch or shrink, and write the equation of a moved parent graph.
I can find the number c from two graphs, and solve an equation with a root function.

Words to know

parent function: The simplest graph of a family: √x, ∛x, 1/x, 2ˣ, log₂x.

shift: Slide the whole graph left, right, up or down.

vertical stretch or shrink: Every output multiplied by the same number.

horizontal stretch or shrink: Every input multiplied by the same number.

asymptote: A line the graph gets closer and closer to.

Common mistakes

Your child moved the graph the wrong way left or right. A number inside with x moves the graph opposite to its sign.

Your child mixed up a left-right move and an up-down move.

Your child mixed up a stretch and a shrink for a number inside with x. Inside, a 3 squeezes the graph toward the y-axis.

What to say

Ask: which x makes the inside 0?

Ask: is the number inside the brackets with x, or outside?

Ask: which input gives the old output now?

Questions parents ask

What is the most common mistake with shifts, flips and stretches of the parent functions: root, reciprocal, exponential and logarithmic?

Your child moved the graph the wrong way left or right. A number inside with x moves the graph opposite to its sign.

How can I help my child with shifts, flips and stretches of the parent functions: root, reciprocal, exponential and logarithmic?

Ask: which x makes the inside 0?

Are these 11th grade math worksheets free to print?

Yes. All 6 printable versions at each level are free to print, with the answer key, and no account is needed.

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