Question

1. a function is shown below.

$f(x) = -\frac{1}{3}x + k$
if $f(21) = 12$, what is the value of $k$?
type a response

Explanation:

Step1: Substitute x = 21 into f(x)

We know that \( f(x)=-\frac{1}{3}x + k \), and when \( x = 21 \), \( f(21)=12 \). So we substitute \( x = 21 \) into the function: \( f(21)=-\frac{1}{3}\times21 + k \)

Step2: Simplify the equation

First, calculate \( -\frac{1}{3}\times21 \). \( -\frac{1}{3}\times21=-7 \), so the equation becomes \( 12=-7 + k \)

Step3: Solve for k

To find k, we add 7 to both sides of the equation: \( k=12 + 7 \)

Step4: Calculate the value of k

\( 12+7 = 19 \), so \( k = 19 \)

Answer:

19