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QuestionFind the linear function ff such that f(1)=4f(1)=4 and f(0)=9f(0)=9. Write f(x)=f(x)=.

Studdy Solution

STEP 1

Assumptions1. The function is linear, which means it can be written in the form f(x)=mx+bf(x) = mx + b, where mm is the slope and bb is the y-intercept. . We have two points on the line (1,4)(1,4) and (0,9)(0,9).

STEP 2

We first need to find the slope of the line, mm. The slope is calculated as the change in yy divided by the change in xx.
m=f(1)−f(0)1−0m = \frac{f(1) - f(0)}{1 -0}

STEP 3

Now, plug in the given values for f(1)f(1) and f(0)f(0) to calculate the slope.
m=−91−0m = \frac{ -9}{1 -0}

STEP 4

Calculate the slope.
m=4−91−0=−m = \frac{4 -9}{1 -0} = -

STEP 5

Now that we have the slope, we can find the y-intercept, bb. Since the line passes through the point (0,9)(0,9), the y-intercept is 99.
b=f(0)=9b = f(0) =9

STEP 6

Now that we have both the slope and the y-intercept, we can write the linear function ff.
f(x)=mx+bf(x) = mx + b

STEP 7

Plug in the values for the slope mm and the y-intercept bb to write the function.
f(x)=−5x+9f(x) = -5x +9So, the linear function ff that has the given function values is f(x)=−5x+9f(x) = -5x +9.

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