Question

graph the equation on paper, and then choose the correct graph.
y = 4^x
choose the correct graph on the right.

Explanation:

Step1: Find y-intercept (x=0)

Substitute $x=0$ into $y=4^x$:
$y=4^0=1$
So the graph passes through $(0,1)$.

Step2: Test positive x-value (x=1)

Substitute $x=1$ into $y=4^x$:
$y=4^1=4$
So the graph passes through $(1,4)$.

Step3: Test negative x-value (x=-1)

Substitute $x=-1$ into $y=4^x$:
$y=4^{-1}=\frac{1}{4}=0.25$
So the graph passes through $(-1, 0.25)$.

Step4: Match to options

This is an increasing exponential function (base $4>1$) that approaches the x-axis as $x\to-\infty$, passes through $(0,1)$, and rises rapidly as $x$ increases. This matches option C.

Answer:

C. <The graph that passes through (0,1), rises from left to right, and approaches the x-axis on the left>