1. **Problem statement:** Given the graph of $f$ with x-intercept $(5,0)$ and y-intercept $(0,8)$, find: (a) The y-intercept of $f(x) + 3$. (b) The y-intercept of $f(4x)$. (c) The x-intercept of $f(2x)$. (d) Describe the transformation $f(x + 1)$. 2. **Recall intercept definitions:** - The y-intercept is the value of the function at $x=0$, i.e., $f(0)$. - The x-intercept is the value of $x$ where $f(x) = 0$. 3. **Given:** - $f(0) = 8$ (y-intercept) - $f(5) = 0$ (x-intercept) 4. **(a) Find y-intercept of $f(x) + 3$:** - Evaluate at $x=0$: $f(0) + 3 = 8 + 3 = 11$ - So, y-intercept is $(0, 11)$. 5. **(b) Find y-intercept of $f(4x)$:** - Evaluate at $x=0$: $f(4 imes 0) = f(0) = 8$ - So, y-intercept is $(0, 8)$. 6. **(c) Find x-intercept of $f(2x)$:** - We want $f(2x) = 0$. - Since $f(5) = 0$, set $2x = 5 ightarrow x = \frac{5}{2} = 2.5$ - So, x-intercept is $(2.5, 0)$. 7. **(d) Describe transformation $f(x + 1)$:** - Replacing $x$ by $x + 1$ shifts the graph **left by 1 unit**. **Final answers:** - (a) y-intercept of $f(x) + 3$ is $(0, 11)$. - (b) y-intercept of $f(4x)$ is $(0, 8)$. - (c) x-intercept of $f(2x)$ is $(2.5, 0)$. - (d) $f(x + 1)$ is the graph of $f$ shifted left by 1 unit.