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JulijaS [17]
2 years ago
13

What is the range of a function f(x)=-x+15 when the domain is {-3,-1,11}?

Mathematics
1 answer:
hodyreva [135]2 years ago
4 0

Answer:

The range is the output value or the y value.

You would work backwards to find the domain.

f(x) = 4x - 1                              f(x) = 4x - 1

3 = 4x - 1                                    7 = 4x - 1

add 1 to both sides                    add 1 to both sides

4 = 4x                                            8 = 4x

divide both sides by 4              divide both sides by 4

x = 1                                              x = 2

f(x) = 4x - 1                                  f(x) = 4x - 1

11 = 4x - 1                                      15 = 4x - 1

add 1 to both sides                      add 1 to both sides

12 = 4x                                              16 = 4x

divide both sides by 4                  divide both sides by 4

x = 3                                                    x = 4

Domain { 1, 2, 3, 4}

Step-by-step explanation:

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3 years ago
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insens350 [35]

Answer:

Question 4:  y=\displaystyle -\frac{4}{5}x

Question 5: y=-5x-3

Step-by-step explanation:

Hi there!

Linear equations are typically organized in slope-intercept form: y=mx+b where <em>m</em> is the slope of the line and <em>b</em> is the y-intercept (the y-coordinate of the point where the line crosses the y-axis).

<u>Question 4</u>

<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>

\displaystyle m=\frac{y_2-y_1}{x_2-x_1} where two points that pass through the line are (x_1,y_1) and (x_2,y_2)

In the graph, two easy-to-identify points on the line are (-5,4) and (5,-4). Plug these into the equation:

\displaystyle m=\frac{-4-4}{5-(-5)}\\\\\displaystyle m=\frac{-4-4}{5+5}\\\\\displaystyle m=\frac{-8}{10}\\\\\displaystyle m=-\frac{4}{5}

Therefore, the slope of the line is \displaystyle -\frac{4}{5}. Plug this into y=mx+b as the slope (<em>m</em>):

y=\displaystyle -\frac{4}{5}x+b

<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>

On the graph, we can see that the line crosses the y-axis when y is 0. Therefore, the y-intercept (<em>b</em>) is 0. Plug this into y=\displaystyle -\frac{4}{5}x+b:

y=\displaystyle -\frac{4}{5}x+0\\\\y=\displaystyle -\frac{4}{5}x

<u>Question 5</u>

<u>1) Determine the slope (</u><u><em>m</em></u><u>)</u>

\displaystyle m=\frac{y_2-y_1}{x_2-x_1}

Two easy-to-identify points are (-1,2) and (0,-3). Plug these into the equation:

\displaystyle m=\frac{-3-2}{0-(-1)}\\\\\displaystyle m=\frac{-3-2}{0+1}\\\\\displaystyle m=\frac{-5}{1}\\\\m=-5

Therefore, the slope is -5. Plug this into y=mx+b:

y=-5x+b

<u>2) Determine the y-intercept (</u><u><em>b</em></u><u>)</u>

On the graph, we can see that the line crosses the y-axis at the point (0,-3). The y-coordinate of this point is -3. Therefore, the y-intercept (<em>b</em>) is -3. Plug this into y=-5x+b:

y=-5x+(-3)\\y=-5x-3

I hope this helps!

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Step-by-step explanation:

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1/2(4)(12) = 24

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