I see that you’ve uploaded an image of a worksheet related to finding intercepts and evaluating functions. Let me extract the details and help you with each section.

1. Top-left corner: Function $f(x) = x - 3$

The task is to find:

• x-intercept: This occurs when $f(x) = 0$. $0 = x - 3 \quad \Rightarrow \quad x = 3$ So, the x-intercept is $(3, 0)$.

• y-intercept: This occurs when $x = 0$. $f(0) = 0 - 3 = -3$ So, the y-intercept is $(0, -3)$.

2. Middle-left graph: Function $f(x) = 2x + 4$

You need to find:

• x-intercept: Set $f(x) = 0$. $0 = 2x + 4 \quad \Rightarrow \quad x = -2$ So, the x-intercept is $(-2, 0)$.

• y-intercept: Set $x = 0$. $f(0) = 2(0) + 4 = 4$ So, the y-intercept is $(0, 4)$.

3. Middle-right graph: Function $f(x) = -3x - 12$

The task is to find:

• x-intercept: Set $f(x) = 0$. $0 = -3x - 12 \quad \Rightarrow \quad x = -4$ So, the x-intercept is $(-4, 0)$.

• y-intercept: Set $x = 0$. $f(0) = -3(0) - 12 = -12$ So, the y-intercept is $(0, -12)$.

4. Bottom-left graph (grid with points)

It looks like you need to evaluate the function at certain points:

• $f(0)$, $f(2)$, and $f(5)$. I will need to zoom in on the graph to confirm, but the general task will involve finding the y-values for these x-values by inspecting the plotted points.

5. Bottom-right section: $f(x) = 2x + 5$

The task is to evaluate the function for several given values:

• $f(0)$: $f(0) = 2(0) + 5 = 5$
• $f(2)$: $f(2) = 2(2) + 5 = 9$
• $f(5)$: $f(5) = 2(5) + 5 = 15$

Do you want further details on any section or help with plotting the graphs? Here are some related questions:

1. How do you calculate intercepts for more complex functions?
2. What is the geometric interpretation of a function’s intercepts?
3. Can you explain how to identify intercepts directly from a graph?
4. What are the practical applications of finding x- and y-intercepts?
5. How does changing the slope affect the intercepts of a linear function?

Tip: For linear functions, remember that the x-intercept tells you when the output is zero, and the y-intercept tells you the function's value when the input is zero.