Question

Please help will mark brainlessness

Answer 1

f(x) y-intercept: 7

f(x) x-intercept: -7/2 or -3.5

g(x) y-intercept: 21

g(x) x-intercept: -7/2 or -3.5

Explanation:

The y-intercept of any function can be found, by substituting in 0 as x. The reason for this is because anywhere on the y-axis, the x-value will be equal to zero. So we know the x-value is going to be zero, we just need to solve for the y-value.

So to find the y-intercept of "g", we simply calculate g(0):\

`g(0) = 3(2(0) + 7)\\\\g(0) = 3(7)\\\\g(0) = 21`

so the y-intercept of the function is 21. Now to find the y-intercept of f, we do the same thing:

`f(0) = 2(0)+7\\\\f(0)=7`

Now to find the x-intercept, we use a similar method. Anywhere on the x-intercept, the y-value is zero, and the x-value may vary. In function notation, the f(x) and g(x) represent the y-value, so we simply substitute it as zero.

To find x-intercept of g, just set g(x) equal to zero:

`0 = 3(2x+7)`

now from here, we usually would have two solutions. Since if one of the factors equals zero, then the entire thing is zero, regardless of the other value.

So let's set the factor (x+7) equal to zero:
`2x+7 = 0\implies 2x = -7\implies x=-(7)/(2)`

let's set 2 equal to zero:
`2=0`, which is of course never true, so we only have the one solution of x = -7

To find the x-intercept of f, do the same process:

`2x+7=0\implies 2x=-7\implies x=- (7)/(2)`