1. The problem is to understand the function $f(x) = 2^x$ with domain $\{1, 2, 3, 4\}$ and find its range and graph points. 2. The formula for an exponential function is $f(x) = a^x$ where $a > 0$ and $a \neq 1$. Here, $a=2$. 3. For each $x$ in the domain, calculate $f(x)$: - $f(1) = 2^1 = 2$ - $f(2) = 2^2 = 4$ - $f(3) = 2^3 = 8$ - $f(4) = 2^4 = 16$ 4. The range is the set of all output values: $\{2, 4, 8, 16\}$. 5. The graph of $y = 2^x$ is an exponential curve passing through points $(1,2)$, $(2,4)$, $(3,8)$, and $(4,16)$. 6. This function maps each input $x$ to exactly one output $y$, confirming it is a function. Final answer: The range of $f(x) = 2^x$ with domain $\{1,2,3,4\}$ is $\{2,4,8,16\}$ and the graph passes through the points mentioned.