Question

The table shows some values of f(x) and g(x) for different values of x:

Answer 1

Answer:

C. x=2

Step-by-step explanation:

To complete the table, let's plug in the x-values into $f(x)$ and $g(x)$, so:

For $f(x)$:

$If \ x=0: \\ \\ f(0)=9(0)+7=7 \\ \\ \\ If \ x=1: \\ \\ f(1)=9(1)+7=16 \\ \\ \\ If \ x=2: \\ \\ f(2)=9(2)+7=25$

For $g(x)$:

$If \ x=-2: \\ \\ g(-2)=5^{-2}=0.04 \\ \\ \\ If \ x=-1: \\ \\ g(-1)=5^{-1}=0.2 \\ \\ \\ If \ x=2: \\ \\ g(2)=5^{2}=25$

From this, the complete table is:

$\left|\begin{array}{c|c|c}x & f(x)=9x+7 & g(x)=5^{x}\\-2 & -11 & 0.04\\-1 & -2 & 0.2\\0 & 7 & 1\\1 & 16 & 5\\2 & 25 & 25\end{array}\right|$

From the table, you can see that $f(x)=g(x)=25$ when $x=2$ so the correct option is C. x=2. But what does $x=2$ mean? It means that at this x-value, the graph of the linear function $f(x)$ and the graph of the exponential function $g(x)$ intersect and the point of intersection is $(2,25)$