Question

Which of the following functions has the greatest y-intercept?

f(x) x y
−3 −14
−2 −6
−1 −2
0 3
1 5
2 6

or g(x) = 3 cos(2x) + 1


please include explanation

Answer 1

the y intercept occurs when x = 0 so in the case of the first function it is y = 3

g(x) = 3 cos 2x + 1

when x = 0 g(x) = 3 cos 0 + 1 = 3*1 + 1 = 4

so the answer is g(x)

Answer 2

g(x) has greatest y-intercept.

Explanation:

We are given a table of values for function f(x) as:

x y=f(x)

−3 −14

−2 −6

−1 −2

0 3

1 5

2 6

We know that the y-intercept of a function is a point where the x-value is zero.

i.e. the input value is zero.

Hence, after looking at the table of values of the function f(x) we have the y-intercept of the function f(x) is:

y=3

Also we are given function g(x) as:

g(x) = 3 cos(2x) + 1

Hence, we calculate the y-intercept of the function g(x) by taking x=0

on taking x=0 we have:

g(0)=3 cos(0)+1

g(0)=3+1=4

Hence, the y-intercept of function g(x) is 4.

Hence, g(x) has the greatest y-intercept.