Find a function whose graph is the given curve.

Question

Find a function whose graph is the given curve.the line segment joining the points (−3, −2) and (−1, 5)

f(x)= ________ for -3 < x < -1

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(Those are less than or equal to signs)

Answer 1

When writing an equation for a line segment, we simply define the line like we would on a normal graph, and add defined endpoints. In this case, those endpoints are given. -3 ≤ x ≤ -1

To write a function, we need the slope and y-intercept. y = mx + b

The slope is the difference in the y-values divided by the difference in the x-values.

5 - (-2) / -1 - (-3)

7/2 = 3.5 - the slope of the line is 3.5

now we have y = 3.5x + b

to find b, plug in one of your ordered pairs for x and y. Let's pick (-1,5)

5 = 3.5*(-1) + b

Now solve for b:

5 = -3.5 + b

8.5 = b

So our function is: y = 3.5x + 8.5