a linear function is given.

Question

(a) Determine the slope and y-intercept of each function.
(b) Use the slope and y-intercept to graph the linear function.
(c) Determine the average rate of change of each function.
(d) Determine whether the linear function is increasing,decreasing,or constant.

f(x) =2x+3

Answer 1

Step 1:

(a) The linear function is .

Compare the function with slope-intercept form of line equation is .

Where, is slope and is  -intercept.

Slope .

-intercept .

Step 2:

(b) Graph the linear function using rise and run:

  - intercept is 3, so the line crosses the - axis at .

Using slope find the next point.

Slope = .

Start at point , move 2 units up and 1 unit right, then plot the point .

 Draw a line through these points.

Step 3:

(c) Slope is the rate of change of linear function.

Average rate of change of a function is .

 Consider and

.

Step 4:

(d) The linear function is

slope of the linear function is is positive.

The function is increasing on .

Solution:

(a) Slope  and  - intercept .

(b) Graph of the function:

(c) The average rate of change is 2.

(d) The function  is increasing on the interval .