Question

Select the correct answer from each drop-down menu. The table represents function f, and the graph represents function g. X -2 -1 0 1 1 2 3 4 No N 7 0 -5 -8 -8 -5

Answer 1

a) The line of symmetry for function f is x = 2, and the line of symmetry for function g is x= 1

b) The y-intercept of function f is is greater than the y-intercept of function g

c) Over the interval [2,4], the average rate of change of function f is less than the average rate of change of the function g

Here, we want to compare some important properties for both functions

We have it as the folllowing;

a) Line of Symmetery

The line of symmetery is that line that divides the quadratic graph into two equal parts of right and left

For the function f, the line of symmetry is x = 2 while the line of symmetry for function g is also x = 1

b) y-intercept

The y-intercept of the function refers to the point at which the graph/plot touches the y-axis

It is the point at which x is 0

For function f, the y-intercept is y = -5

For function g, the y-intercept is y = -6

c) Average rate of change

The average rate of change of a function over an interval [a,b] can be calculated using the formula;

`(f(b)-f(a))/(b-a)`

According to thisn question, a is 2 while b is 4

For the function f; f(2) is -9 while f(4) is -5

For the function g; g(2) is -6 while g(4) is 2

So the average rate of change for the function f on the interval is;

`(-5+9)/(4-2)\text{ = 2}`

For the function g, the average rate of change on the interval is;

`(2+6)/(4-2)\text{ =}(8)/(2)\text{ = 4}`