Question

1. (1.3) using the graph below, fill in each of the key features in function notation

function: (circle one) yes or no
domain:
range:
maximum:
minimum:
interval(s) of increase:
interval(s) of decrease:
x - intercept:
y - intercept:

Explanation:

Step1: Identify domain

The graph exists for all x - values from - 10 to 10. So the domain is $[-10,10]$.

Step2: Identify range

The lowest y - value is - 3 and the highest is 7. So the range is $[-3,7]$.

Step3: Find maximum

The highest point on the graph has a y - value of 7. So the maximum is 7.

Step4: Find minimum

The lowest points on the graph have a y - value of - 3. So the minimum is - 3.

Step5: Find intervals of increase

The graph is increasing when the y - values are getting larger as x increases. The intervals are $[-7,-5]$ and $[6,10]$.

Step6: Find intervals of decrease

The graph is decreasing when the y - values are getting smaller as x increases. The intervals are $[-10,-7]$ and $[1,6]$.

Step7: Find x - intercepts

The points where the graph crosses the x - axis are approximately $x=-6,x = 0,x = 4$.

Step8: Find y - intercept

The point where the graph crosses the y - axis is at $y = 0$.

Answer:

Domain: $[-10,10]$
Range: $[-3,7]$
Maximum: 7
Minimum: - 3
Interval(s) of increase: $[-7,-5],[6,10]$
Interval(s) of decrease: $[-10,-7],[1,6]$
x - intercept: $x=-6,x = 0,x = 4$
y - intercept: $y = 0$