1. **Problem Statement:** Given the function $f(x) = 3x + 3$, find: (a) the $x$-intercept and $y$-intercept, (b) zeros of the function, (c) asymptotes. 2. **Formula and Rules:** - The $x$-intercept occurs where $f(x) = 0$. - The $y$-intercept occurs where $x = 0$. - Zeros of the function are values of $x$ where $f(x) = 0$. - Asymptotes are lines the graph approaches but never touches; linear functions have no asymptotes. 3. **Finding the $x$-intercept:** Set $f(x) = 0$: $$3x + 3 = 0$$ Subtract 3 from both sides: $$3x = -3$$ Divide both sides by 3: $$x = -1$$ So, the $x$-intercept is at $(-1, 0)$. 4. **Finding the $y$-intercept:** Set $x = 0$: $$f(0) = 3(0) + 3 = 3$$ So, the $y$-intercept is at $(0, 3)$. 5. **Finding zeros:** Zeros are where $f(x) = 0$, which we already found as $x = -1$. 6. **Asymptotes:** Since $f(x)$ is a linear function, it has no asymptotes. **Final answers:** (a) $x$-intercept: $(-1, 0)$, $y$-intercept: $(0, 3)$ (b) Zero: $x = -1$ (c) No asymptotes