Answer:
(d) -1.75
Explanation:
You want to find the y-value where f(x) = g(x) for these functions:
- f(x) = 2x³ +2x -3
- g(x) = -0.5|x -4|
Estimate
The function f(x) has its y-intercept at f(0) = -3. For x=1, the y-value is ...
f(1) = 2 +2 -3 = 1
That is, it is between -3 and 1 for x between 0 and 1.
The function g(x) has no positive values, eliminating choices A and C. Its y-intercept is g(0) = -2, and for x=1 its value is g(1) = -1.5.
This tells you that the two function values will be equal for some y-value between -2 and -1.5, eliminating choice B.
The only reasonable choice is D, y = -1.75.
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Additional comment
The attachment shows that a graphing calculator confirms this value.
You can often tell a lot about where function graphs will intersect by considering the x- and y-intercepts, or a couple of points on either side of the intersection. That is what we have done here.
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