Here’s the detailed breakdown of the questions from the image:

For (1):

(a) Is it linear or nonlinear?

• The graph shows a curve that is not straight, so it is nonlinear.

(b) Is it a function?

• To check if it is a function, use the vertical line test. If a vertical line intersects the curve at more than one point, it is not a function. For (1), the graph passes the vertical line test, so it is a function.

For (2):

(a) Is it linear or nonlinear?

• The graph is a curve and not a straight line, so it is nonlinear.

(b) Is it a function?

• Using the vertical line test, a vertical line intersects the graph in more than one place. Therefore, it is not a function.

For (3): $y = 5x - 3$

This is a linear equation in slope-intercept form $y = mx + b$, where:

• $m$ (slope) = 5
• $b$ (y-intercept) = -3

Would you like me to go into more detail about these solutions or how I derived them?

Follow-Up Questions:

1. How do you apply the vertical line test to determine if a curve is a function?
2. What defines a function as linear or nonlinear?
3. How can you graph a linear equation such as $y = 5x - 3$?
4. What is the significance of the slope ($m$) and intercept ($b$) in the equation $y = mx + b$?
5. Could a graph ever fail both the linearity and function tests? Why?

Tip:

To quickly check if a graph represents a function, imagine drawing vertical lines across it. If any line touches the graph more than once, it's not a function!