Question

The illustration below shows the graph of y as a function of x.

Complete the following sentences based on the graph of the function.

. as X increases Y:
.the rate of change for y as a function of x is: ,therefore the function is
.for all values of x, the function value y: ,0
.The y-intercept of the graph is the function value y=:
.

Answer 1

1. decreases

2. not constant, not linear

3. greater than

4. y=8

Explanation:

1. As the x- values increase, the y- values decrease. Here's some data. When x is 1, y is 5. When x goes up to 2, y goes down to 3.

2. We need to calculate the rate of change; how much does y change per unit of x? When X is 0, y is 8, when x is 1, y is 5, and when x is 2, y is 3. From 8 to 5 is three units. From 5 to 3 is two units. Remember that for both of these scenarios, x only changed by ONE UNIT. Therefore, the rate of change is not constant. (Rate of change is ONLY constant for linear equations) So, if the rate of change is NOT constant, then the function must NOT be linear!

3. This is an exponential function, and it has a horizontal asymptote at y=0. This means that all the y- values must be ABOVE zero. This isn't necessary, but it helps: The range for this function is (0, infinity).

4. To find the y- intercept, we just see where the graph intersects with the y- axis. For this graph, the graph intersects the y- axis at 8, so y=8.

Hope this helped!!!