Question 1

Given $$f(x) = x^2$, which sequence of transformations produces g(x$$) = $$-x^2 - 3$?

Accepted Answer

Reflect across the x-axis, then translate down 3 units

Question 2

If $$f(x) = \sqrt{x}$$, what is the equation for $$g(x)$$ after reflecting across the y-axis, stretching vertically by a factor of 2, and translating down 3 units?

Accepted Answer

$$g(x) = 2\sqrt{-x} - 3$$

Question 3

Which transformation(s) are needed to change $$f(x) = x$$ into $$g(x) = 3x + 1$$?

Accepted Answer

Stretch vertically by a factor of 3 and translate up 1 unit

Question 4

Given $$f(x) = x^2$, what is the result of translating right 1 unit and down 3 units?

Accepted Answer

$$g(x) = (x - 1)^2$ - 3$$

Question 5

If $$f(x) = x$$, what is the equation for $$g(x)$$ after stretching horizontally by a factor of 3 and translating left 1 unit?

Accepted Answer

$$g(x) = \frac{1}{3}(x + 1)$$

Question 6

Which transformation(s) are needed to change $$f(x) = \sqrt{x}$$ into $$g(x) = -\sqrt{-x - 2}$$?

Accepted Answer

Reflect across the y-axis, reflect across the x-axis, translate right 2 units

Question 7

Given $$f(x) = x^2$, what is the effect of compressing horizontally by a factor of 2 and reflecting across the x-axis?

Accepted Answer

$$g(x) = -(2x)^2$

Question 8

If $$f(x) = \sqrt{x}$$, what is the equation for $$g(x)$$ after stretching horizontally by a factor of 3, reflecting across the x-axis, and translating down 3 units?

Accepted Answer

$$g(x) = -\sqrt{\frac{x}{3}} - 3$$

Question 9

Which transformation(s) are needed to change $$f(x) = x$$ into $$g(x) = x - 2 - 1$$?

Accepted Answer

Translate right 2 units, then down 1 unit

Question 10

Given $$f(x) = \sqrt{x}$$, what is the result of reflecting across the y-axis and translating down 1 unit?

Accepted Answer

$$g(x) = \sqrt{-x} - 1$$

Question 11

If $$f(x) = x$$, what is the equation for $$g(x)$$ after compressing vertically by a factor of 2 and translating left 3 units?

Accepted Answer

$$g(x) = \frac{1}{2}(x + 3)$$

Question 12

A medical researcher models the spread of a virus using $$f(x) = x^2$. If the virus spreads twice as fast and the number of cases is inverted, what is the new function?

Accepted Answer

$$g(x) = -(2x)^2$

Question 13

Given $$f(x) = \sqrt{x}$$, what is the equation for $$g(x)$$ after reflecting across the y-axis, stretching vertically by a factor of 2, and translating down 3 units?

Accepted Answer

$$g(x) = 2\sqrt{-x} - 3$$

Question 14

A chemical reaction is modeled by $$f(x) = x. If $$the reaction rate is stretched horizontally by a factor of 3 and shifted left by 1 unit, what is the new function?

Accepted Answer

$$g(x) = \frac{1}{3}(x + 1)$$

Question 15

If $$f(x) = x$$, what is the equation for $$g(x)$$ after stretching vertically by a factor of 3 and translating up 1 unit?

Accepted Answer

$$g(x) = 3x + 1$$

Question 16

Given $$f(x) = x^2$, what is the result of compressing horizontally by a factor of 2 and reflecting across the x-axis?

Accepted Answer

$$g(x) = -(2x)^2$

Question 17

A population model uses $$f(x) = x^2$. If the population is shifted right by 1 unit and down by 3 units, what is the new function?

Accepted Answer

$$g(x) = (x - 1)^2$ - 3$$

Algebra 2 Transformations Practice – Step-by-Step Guidance

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