Question

find the value of k or h in each of the graphs.
6.
$g(x)=3^x + k$
$f(x)=3^x$
7.
$f(x)=3^x$
$g(x)=3^{x-h}$

Explanation:

Step1: Solve for k (Problem 6)

Identify a shared x-value: take $x=0$. For $f(x)=3^x$, $f(0)=3^0=1$. From the graph, $g(0)=3$. Substitute into $g(x)=3^x+k$:
$3 = 3^0 + k$
$3 = 1 + k$
$k = 3 - 1 = 2$

Step2: Solve for h (Problem 7)

Identify a shared y-value: take $y=1$. For $f(x)=3^x$, $3^x=1$ gives $x=0$. From the graph, $g(x)=1$ when $x=1$. Substitute into $g(x)=3^{x-h}$:
$1 = 3^{1-h}$
Since $3^0=1$, $1-h=0$
$h = 1$

Answer:

For problem 6: $k=2$
For problem 7: $h=1$