Question

function 3
graph of function 3
○ linear
○ not linear
function 4
graph of function 4
○ linear
○ not linear

Explanation:

For Function 3:

Step1: Recall linear function definition

A linear function has a constant rate of change and its graph is a straight line (or can be represented as \( y = mx + b \), where \( m \) (slope) and \( b \) (y - intercept) are constants).

Step2: Analyze the graph of Function 3

The graph of Function 3 is a curve with multiple turning points (it goes up, then down, then up again). It does not have a constant slope, and its shape cannot be represented by the equation of a straight line (\( y=mx + b \)). So, Function 3 is not linear.

For Function 4:

Step1: Recall linear function definition

A linear function has a constant rate of change and its graph is a straight line (or can be represented as \( y=mx + b \), where \( m \) (slope) and \( b \) (y - intercept) are constants).

Step2: Analyze the graph of Function 4

The graph of Function 4 is a curve with multiple peaks and troughs (it oscillates). It does not have a constant slope, and its shape cannot be represented by the equation of a straight line (\( y = mx + b \)). So, Function 4 is not linear.

Answer:

Function 3: Not linear
Function 4: Not linear