Josie wrote the function f(x)=(x-4)(x-3)(x+2) to model the graph below. Explain where Josie went wrong.

Question

https://imgur.com/a/tgQmRio

here is the graph given

Answer 1

Make a table substituting values of x to find f(x):

Looking at the function, we understand that f(x)=0 when x = -2, 3 and 4.

x = -3 : f(x) = -42

x = -2 : f(x) = 0

x = -1 : f(x) = 20

x = 0 : f(x) = 24

x = 1 : f(x) = 18

x = 2 : f(x) = 8

x = 3 : f(x) = 0

x = 4 : f(x) = 0

Using the values of f(x), graph the function.

The function has 3 roots/zeroes. Plot these three points first. x=-2,3,4.

Then to understand the behavior of the function, select one value each between these points.

Take x < -2:

x-4 is negative

x-3 is negative

x+2 is negative.

Therefore, product of the above three expressions f(x) is negative for x<-2.

Similarly:

Take -2<x<3:

x-4 is negative

x-3 is negative

x+2 is positive.

Therefore, product of the above three expressions f(x) is positive for -2<x<3.

Take 3<x<4

x-4 is negative

x-3 is positive

x+2 is positive.

Therefore, product of the above three expressions f(x) is negative for 3<x<4.

Take x>4

x-4 is positive

x-3 is positive

x+2 is positive.

Therefore, product of the above three expressions f(x) is positive for x>4.

Notice how the graph increases/decreases and has positive/negative values.

Now, we have all the information to draw the graph. :)

<I'm sorry I'm unable to upload an image of the graph here.>

Hope this helps. Please do not hesitate to ask if you have any further questions. :)

Regards,

Rupa.