Question

which is the graph of $f(x) = 4^x$?

Explanation:

Step1: Identify function type

$f(x)=4^x$ is an exponential function with base $4>1$.

Step2: Key properties of the function

1. When $x=0$, $f(0)=4^0=1$, so the graph passes through $(0,1)$.
2. As $x\to+\infty$, $f(x)\to+\infty$ (increasing rapidly).
3. As $x\to-\infty$, $f(x)\to0$ (approaches x-axis from above).

Step3: Match with given graphs

The left graph passes through $(0,1)$, increases for positive $x$, and approaches the x-axis for negative $x$. The right graph is a parabola (quadratic function, not exponential).

Answer:

The graph on the left (the exponential curve passing through (0,1), increasing upwards on the right, and approaching the x-axis on the left) is the graph of $f(x)=4^x$.