1. The problem is to understand and graph the function $g(x) = 2^x - 1 + 3$. 2. First, simplify the function by combining like terms: $$g(x) = 2^x - 1 + 3 = 2^x + 2$$ 3. This is an exponential function of the form $g(x) = a^x + c$ where $a=2$ and $c=2$. 4. Important rules for exponential functions: - The base $a=2$ means the function grows exponentially as $x$ increases. - The $+2$ shifts the entire graph vertically upward by 2 units. 5. To find the y-intercept, set $x=0$: $$g(0) = 2^0 + 2 = 1 + 2 = 3$$ 6. The graph crosses the y-axis at $y=3$, which matches the description. 7. For other values: - At $x=1$, $g(1) = 2^1 + 2 = 2 + 2 = 4$ - At $x=2$, $g(2) = 2^2 + 2 = 4 + 2 = 6$ - At $x=3$, $g(3) = 2^3 + 2 = 8 + 2 = 10$ 8. The graph increases sharply upward as $x$ increases, consistent with the exponential growth. Final answer: The graph of $g(x) = 2^x + 2$ is an exponential curve shifted up by 2 units, crossing the y-axis at 3 and increasing rapidly for positive $x$ values.