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Use the given function to complete parts a) through e) below.

[tex]\[ f(x) = -x + 2 \][/tex]

a) Describe the end behavior of the function.

D. The graph of [tex]\( f(x) \)[/tex] rises to the left and falls to the right.

b) Find the x-intercepts.

[tex]\[ x = \][/tex]
(Type an integer or a decimal. Use a comma to separate answers as needed.)



Answer :

GinnyAnswer
Sure! Let's solve the problem step-by-step.

We are given the function:

[tex]\[ f(x) = -x + 2 \][/tex]

Part (b) asks us to find the x-intercepts. The x-intercepts are the points where the graph of the function crosses the x-axis. This occurs where [tex]\( f(x) = 0 \)[/tex].

To find the x-intercepts, we solve the equation:

[tex]\[ f(x) = 0 \][/tex]
[tex]\[ -x + 2 = 0 \][/tex]

Now, solve for x:

[tex]\[ -x + 2 = 0 \][/tex]
[tex]\[ -x = -2 \][/tex]
[tex]\[ x = 2 \][/tex]

Therefore, the x-intercept of the function [tex]\( f(x) = -x + 2 \)[/tex] is:

[tex]\[ x = 2 \][/tex]

So, the answer is:
[tex]\[ X = 2 \][/tex]

This means that the graph of the function crosses the x-axis at [tex]\( x = 2 \)[/tex].

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