Need to find x and y intercepts for f(x)=-(1/8)(x-1)^5+5

C

Christ

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My son and I can't figure this one out. Any help is appreciated.

Thanks,
Christopher D
 
Staring into the interior of the function, it appear that x = 1 would be a good place to find an x-intercept. Substitute x = 1 and you will see it.

If x = 0 is in the Domain, substitute x = 0 to find any y-intercept.
 
f(x) = -(1/8)(x-1)^5 + 5
Click to expand...

Please verify that you have correctly typed the function above. I'm looking at the exponent 5 thinking that maybe it's supposed to be 2.
 
tkhunny said:
Staring into the interior of the function, it appear that x = 1 would be a good place to find an x-intercept.
Click to expand...
Why? I was under the impression that the x-intercept was where y= 0 and that does not have anything to do with x= 1.

Substitute x = 1 and you will see it.

If x = 0 is in the Domain, substitute x = 0 to find any y-intercept.
Click to expand...
 
mmm4444bot said:
Please verify that you have correctly typed the function above. I'm looking at the exponent 5 thinking that maybe it's supposed to be 2.
Click to expand...
I see no reason to assume that. At the x-intercept, f(x)= -(1/8)(x- 1)^5+ 5= 0 so we have (x- 1)^5= 40 and then take the fifth root. No harder, certainly, than taking the square root.

The y-intercept is where x= 0 so it becomes a simple matter of integer arithmetic.
 
Whoops! (This is one of those simple exercises that bites me back because I respond without actually putting any pencil to paper.)

Somehow, I stopped thinking x-intercept and started thinking that the exercise called for the roots (most of which are Complex imaginary).

My bad. Thank you for catching that.

(Maybe TK missed the + 5 part, in his response?)
 
Christ said:
My son and I can't figure this one out.
Click to expand...

Okay -- I goofed, but you and your son need to memorize the following. :cool:


ALL x-intercepts have coordinates of this form: (x, 0)

ALL y-intercepts have coordinates of this form: (0, y)


In other words, if you're looking for an x-intercept, then y = 0.

If you're looking for a y-intercept, then x = 0.

Always!


This makes clear sense, if you think graphically. For example, an x-intercept is the point where a graph intersects the x-axis. If the y-coordinate is not zero, then it is impossible for that point to be on the x-axis.

Similar logic applies to y-intercepts.


Cheers!
 
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