Find g(x), where g(x) is the translation 9 units down of f(x) = 10x + 8. Choices: [[g(x) = 10x – 82][g(x) = 10x + 98][g(x) = 10x – 1][g(x) = 10x + 17]]

Understand transformation rule: Understand the transformation rule for translating a function vertically. To translate a function k units down, we subtract k from the original function f(x). Transformation rule: g(x) = f(x) - kApply rule to given function: Apply the transformation rule to translate f(x) = 10x + 8, 9 units down. We know that k = 9 for this problem, so we substitute 9 for k in the transformation rule. g(x) = f(x) - 9Substitute function into rule: Substitute the given function f(x) into the transformation rule to find g(x). We have f(x) = 10x + 8, so we substitute this into g(x) = f(x) - 9. g(x) = (10x + 8) - 9Simplify expression for g: Simplify the expression for g(x) by combining like terms. g(x) = 10x + 8 - 9 g(x) = 10x - 1

Resources

Testimonials

Plans

Resources

Testimonials

Plans

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Find $g(x)$ , where $g(x)$ is the translation $9$ units down of $f(x) = 10x + 8$ . $\newline$ Choices: $\newline$ (A) $g(x) = 10x - 82$ $\newline$ (B) $g(x) = 10x + 98$ $\newline$ (C) $g(x) = 10x - 1$ $\newline$ (D) $g(x) = 10x + 17$

View step-by-step help

Home

Math Problems

Algebra 2

Transformations of functions

Full solution

Q. Find

g(x)

, where

g(x)

is the translation

9

units down of

f(x) = 10x + 8

\newline

Choices:

\newline

(A)

g(x) = 10x - 82

\newline

(B)

g(x) = 10x + 98

\newline

(C)

g(x) = 10x - 1

\newline

(D)

g(x) = 10x + 17

Understand transformation rule: Understand the transformation rule for translating a function vertically. $\newline$ To translate a function $k$ units down, we subtract $k$ from the original function $f(x)$ . $\newline$ Transformation rule: $g(x) = f(x) - k$
Apply rule to given function: Apply the transformation rule to translate $f(x) = 10x + 8$ , $9$ units down. $\newline$ We know that $k = 9$ for this problem, so we substitute $9$ for $k$ in the transformation rule. $\newline$ $g(x) = f(x) - 9$
Substitute function into rule: Substitute the given function $f(x)$ into the transformation rule to find $g(x)$ . We have $f(x) = 10x + 8$ , so we substitute this into $g(x) = f(x) - 9$ . $g(x) = (10x + 8) - 9$
Simplify expression for $g$ : Simplify the expression for $g(x)$ by combining like terms. $\newline$ $g(x) = 10x + 8 - 9$ $\newline$ $g(x) = 10x - 1$