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He function f(x) is graphed on the coordinate plane.

What is f(−4)?



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f(−4) =

Graph of a line on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A line passes through the points begin ordered pair 0 comma 2 end ordered pair and begin ordered pair 4 comma 0 end ordered pair.

User Amol Katdare
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2 Answers

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24 votes

Final answer:

To find f(−4), we use the points (0, 2) and (4, 0) to calculate the slope of the line, which is -1/2. With the y-intercept of 2, we form the equation y = -1/2x + 2 and find that f(−4) = 4.

Step-by-step explanation:

To determine f(−4), we need to find the value of the function f(x) at x = −4. According to the given description, the graph of the line passes through the points (0, 2) and (4, 0). We can use these points to find the slope of the line, which is necessary for calculating f(x) at any given x-value.

To calculate the slope (m), we use the formula:

m = (y2 - y1) / (x2 - x1)

By substituting the given points:

m = (0 - 2) / (4 - 0) = -2 / 4 = -1/2

Now we have the slope. The y-intercept is given directly by the point (0, 2), which means b = 2. Using the general form of a straight line equation y = mx + b, we now have:

y = -1/2x + 2

To find f(−4), we simply substitute x = −4 into our equation:

f(−4) = -1/2(-4) + 2 = 2 + 2 = 4

Therefore, f(−4) = 4.

User Simon Heinzle
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15 votes
15 votes

Answer: f (-4) = 4

so the answer is 4

User Nate Murray
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