Express the function graphed on the axes below as a piecewise function.
1 answer:
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Answer:
{-1, 1/2, 2/3, 1}
Step-by-step explanation:
I find a graphing calculator to be a most useful tool for problems like this. (See attached.)
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First of all, observe that the constant is -2, so 0 is not a zero.
It is often useful to look at the sum of coefficients. Here, that is 0, indicating 1 is a zero.
You can divide that out, or simply continue by looking at the sum of coefficients with odd-degree terms negated. Then you have 6 +7 -4 -7 -2 = 0, indicating -1 is also a zero.
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At this point, it can be useful to divide out the factors you know. The synthetic division tableaus attached show that work. First is division by (x+1), then by (x -1).
The result of doing that is the quadratic ...
6x^2 -7x +2 = 0
This can be factored ...
(6x^2 -3x) -(4x -2) = 0 . . . . . . rewrite -7x and group term pairs
3x(2x -1) -2(2x -1) = 0 . . . . . . . factor each pair
(3x -2)(2x -1) = 0 . . . . . . the factorization of the remaining quadratic
The zeros of this are the values of x that make the factors zero: 2/3 and 1/2.
The zeros of the given function f(x) are x ∈ {-1, 1/2, 2/3, 1}.
<h3>Answer:</h3>
A. y = -1/3x + 2 . . . . . . . . assuming a typo in your problem statement
<h3>Explanation:</h3>The point (0, 2) is the y-intercept. This tells you the equation will be something of the form ...
... y = mx + 2 . . . . . . matching only answer choices A and C
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Knowing this, you can either substitute the values x=3, y=1 into these two equations to see which one works (it is not C), or you can look at the two points and determine the value of the slope.
The slope is ...
... (difference in y)/(difference in x) = (1-2)/(3-0) = -1/3 . . . . . matches choice A
The equation of the line is ...
... y = -1/3x + 2 . . . . . matches answer choice A