Question

Suppose that the x-intercepts of a graph of y = f(x) are -9, and -5

What are the intercepts of a graph of y = 5f(x) ?

Answer 1

ugh algebra :/

Answer 2

Let's make up a function that has those x intercepts and find out.

Answer 3

y=f(x)=(x+9)(x+5)

Answer 4

Would you agree that the x intercepts of that function are -9 and -5?

Answer 5

yes

Answer 6

would
i just apply
= 5(x+9) 5(x+5)

Answer 7

Ok. Let's multiply it by 5 and see what happens: 5y=5f(x)=5(x+9)(x+5)

Answer 8

What are the x intercepts of the new function?

Answer 9

5x + 45 ?
5x + 25?

Answer 10

Have you heard of the concept that "if the product of factors is 0 then one of the factors must be 0"?

Answer 11

i haven't, but it makes sense

Answer 12

Then why did you say that the x intercepts of y = (x+9)(x+5) are -9 and -5 if you don't know that concept?

Answer 13

i am just very confused.. hah . sorry

Answer 14

x intercepts are found by letting y be 0 and solving for x.

Answer 15

i can do it if the number is after the equation or inside, i just dont understand what it means when the number comes before the f(x)

Answer 16

That means multiply the function by 5

Answer 17

what will happen to the graph in that case then. does it expand?

Answer 18

Here is what you need to learn: (x+9)(x+5)= 0 means that x +9=0 or x+5=0

Answer 19

If you multiply that function by 5 you have: 5(x+9)(x+5)=0 and that means that 5 = 0 or x+9=0 or x+5=0

Answer 20

Obviously 5 cannot equal 0 so it must be true the x+9=0 or x+5=0. In other words, the x intercepts do not change. It just means that the function undergoes a stretch factor of 5

Answer 21

ok so the intercepts for this one would be -9 and -5

Answer 22

yep

Answer 23

im going to go draw the graph to get a visual of the stretch factor, other than that i think i understand

Answer 24

thank you

Answer 25

yw. Just use your graphing calculator and you will see that they are both parabolas but that the second one is really skinny.