SOLUTION: Find the x-intercepts (horizontal intercepts) of the function: f(x)=4|x−3|−1 The intercepts are at x=

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Question 1187171: Find the x-intercepts (horizontal intercepts) of the function:
f(x)=4|x−3|−1
The intercepts are at x=
Found 4 solutions by MathLover1, Theo, Alan3354, ikleyn:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

Find the x-intercepts (horizontal intercepts) of the function:

set

......................recall that





and






The intercepts are at and

Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the x-intercept is the value of x when the value of y = 0.

the equation is f(x) = 4 * |x - 3| - 1.
set y = f(x) and the equation becomes y = 4 * |x - 3| - 1.
set y equal to 0 and the equation becomes 0 = 4 * |x - 3| - 1.
this is the same as 4 * |x - 3| - 1 = 0.
add 1 to both sides of the equation to get 4 * |x - 3| = 1.
divide both sides of the equation by 4 to get |x - 3| = 1/4.
when the expression within the absolute value sign is positive, the equation becomes x - 3 = 1/4.
add 3 to both sides to get x = 3 + 1/4 = 13/4.
when the expression within the absolute value sign is negative, the equation becomes -(x-3) = 1/4.
simplify to get -x + 3 = 1/4
subtract 3 from both sides to get -x = -3 + 1/4
multiply both sides by -1 to get x = 3 - 1/4 = 2 + 3/4 = 11/4.

the x-intercept should be x = 11/4 or and x = 13/4.

when x = 11/4, the equation becomes f(x) = 4 * abs(11/4 - 3) - 1 which becomes f(x) = 4 * abs(11/4 - 12/4) - 1 which becomes f(x) = 4 * 1/4 - 1 which becomes f(x) = 0.
when x = 13/4, the equation becomes f(x) = 4 * abs(13/4 - 3) - 1 which becomes f(x) = 4 * abs(13/4 - 12/4) - 1 which becomes f(x) = 4 * 1/4 - 1 which becomes f(x) = 0.

both values of x are confirmed to be good.

your solution is that the y-intercepts are at x = 11/4 and x = 13/4.

abs(x-3) means the same thing as |x-3|.

the equation was graphed and is shown below.



11/4 = 2.75 as shown on the graph.
13/4 = 3.25 as shown on the graph.
Answer by Alan3354(69443)   (Show Source): You can put this solution on YOUR website!
There is no such thing as a "horizontal intercept."
Answer by ikleyn(52835)   (Show Source): You can put this solution on YOUR website!
.
Find the x-intercepts (horizontal intercepts) of the function:
f(x)=4|x−3|−1
The intercepts are at x=
~~~~~~~~~~~~~~~ 

x-intercepts are the zeros of the function f(x),  i.e. the roots of the equation f(x) = 0,  which is

    4*|x-3| - 1 = 0.


It is equivalent to  

    4*|x-3| = 1,   or   |x-3| = .


The last equation describes the points in the number line that are remoted exactly 0.25 units from the number (point) 3.

So, its roots are  3-0.25 = 2.75  and/or  3+0.25 = 3.25.


ANSWER.  The sough x-intercepts are the points  2.75  and  3.75  of x-axis.

Solved.



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