1. What are the solutions (coordinate points) to the system of equations?
y=x^2+5x+6 and y=3x+6

2. Prove algebraically what type of function this is (even, odd, or neither).
f(x)=x^6-x^4

3. Given the function f(x)=x^2+3x-2
What is the average rate of change for the function from 2 to 6? Show your work.

Question 1

The given system of equations is:

Equate the two equations:

Rewrite in standard form:

When we put x=0, in y=3x +6, we get:

One solution is (0,6)

When we put x=-2, into y=3x+6, we get:

Another solution is (-2,0)

The solutions are; (0,6) and (-2,0)

Question 2:

The function is

Let us put x=-x,

This gives:

We can observe that:

This is the property of an even function.

Question 3:

The given function is

The average rate of change of f(x) from x=a to x=b is given as:

This is the slope of the secant line connecting the two points on f(x)

From x=2 to x=6, the average rate of change

The average rate of change is 11

n

step-by-step explanation: