What kind of transformation converts the graph of f(x) = -7(x - 5)^2 + 2 into the graph of g(x) = -7(x - 5)^2 + 5? Choices: (A)translation 3 units right (B)translation 3 units down (C)translation 3 units up (D)translation 3 units left

Identify Transformation Type: Analyze the given functions f(x) = -7(x - 5)^2 + 2 and g(x) = -7(x - 5)^2 + 5 to determine the type of transformation. Notice that the only difference between f(x) and g(x) is the constant term at the end of the equation. This indicates a vertical shift.Determine Vertical Shift Direction: Determine the direction of the vertical shift. Since the constant term in g(x) is greater than the constant term in f(x) (5 > 2), the graph of f(x) has been shifted upwards to become g(x).Calculate Shift Magnitude: Calculate the magnitude of the vertical shift. Subtract the constant term of f(x) from the constant term of g(x) to find the magnitude of the shift: 5 - 2 = 3. This means the graph has been shifted 3 units up.

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

What kind of transformation converts the graph of $f(x) = -7(x - 5)^2 + 2$ into the graph of $g(x) = -7(x - 5)^2 + 5$ ? $\newline$ Choices: $\newline$ (A) translation $3$ units right $\newline$ (B) translation $3$ units down $\newline$ (C) translation $3$ units up $\newline$ (D) translation $3$ units left

View step-by-step help

Home

Math Problems

Algebra 1

Describe function transformations

Full solution

Q. What kind of transformation converts the graph of

f(x) = -7(x - 5)^2 + 2

into the graph of

g(x) = -7(x - 5)^2 + 5

\newline

Choices:

\newline

(A) translation

3

units right

\newline

(B) translation

3

units down

\newline

3

units up

\newline

(D) translation

3

units left

Identify Transformation Type: Analyze the given functions $f(x) = -7(x - 5)^2 + 2$ and $g(x) = -7(x - 5)^2 + 5$ to determine the type of transformation. $\newline$ Notice that the only difference between $f(x)$ and $g(x)$ is the constant term at the end of the equation. This indicates a vertical shift.
Determine Vertical Shift Direction: Determine the direction of the vertical shift. Since the constant term in $g(x)$ is greater than the constant term in $f(x)$ (5 > 2), the graph of $f(x)$ has been shifted upwards to become $g(x)$ .
Calculate Shift Magnitude: Calculate the magnitude of the vertical shift. Subtract the constant term of $f(x)$ from the constant term of $g(x)$ to find the magnitude of the shift: $5 - 2 = 3$ . This means the graph has been shifted $3$ units up.