Question

find the value of k or h in each of the graphs.
see examples 1–3
23.
$g(x) = 3^x + k$
$f(x) = 3^x$

Explanation:

Step1: Find the y-intercept of \( f(x) = 3^x \)

For \( f(x) = 3^x \), when \( x = 0 \), \( f(0)=3^0 = 1 \).

Step2: Find the y-intercept of \( g(x) = 3^x + k \)

For \( g(x) = 3^x + k \), when \( x = 0 \), \( g(0)=3^0 + k = 1 + k \). From the graph, the y - intercept of \( g(x) \) is 3 (since at \( x = 0 \), the blue curve \( g(x) \) passes through \( (0,3) \)). So we set up the equation \( 1 + k=3 \).

Step3: Solve for \( k \)

Subtract 1 from both sides of the equation \( 1 + k = 3 \). We get \( k=3 - 1=2 \).

Answer:

\( k = 2 \)