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2 years ago

Which of the following is the graph of f(x) = -0.5|x+3| -2?

Mathematics

2 answers:

Tcecarenko [31]2 years ago

7 0

Answer:

The last graph

Step-by-step explanation:

We transform functions in the following ways:

multiplying the function by a number to stretch or shrink it
multiplying by a negative to flip the orientation of the function
adding/subtracting a value to the input x to shift it horizontally
adding/subtracting a value to the output (or outside the function operation) to shift it vertically or horizontally.

Looking at the equation we can see $f(x)=-0.5\left|x+3\right|-2$

Vertically shrunk by 0.5
Negative leading coefficient to flip the graph's orientation
Horizontal shift of the vertex of 3 units to the left from (0,-2) to (-3,-2)
Vertical shift of the vertex of 2 units downward (-3,0) to (-3,-2)

The last graph has vertex (-3,-2) and satisfies the the equation.

emmasim [6.3K]2 years ago

5 0

Answer: first one

Step-by-step explanation:

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2 years ago

Read 2 more answers

Find the equation of the line that is perpendicular to the line 4x+2y=1 and passes through the point (-4,3)

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First find the slope of the given line:

4x +2y = 1

Subtract 4x from each side:

2y = -4x + 1

Divide both sides by 2:

y = -2x +1/2

The slope is -2.

Now use the slope to find the y-intercept. Because the line is perpendicular, you need to use the negative inverse of the slope.

The negative inverse of -2 is 1/2

Now using the point-slope form y - y1 = m(x-x1)

Use the inverse slope for m, and the given point(-4,3) to get:

y - 3 = 1/2(x+4)

Simplify:

y - 3 = x/2 +2

Add 3 to each side:

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Reorder the terms to get y = 1/2x +5

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3 years ago

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3 years ago

If the domain of the function f(x)=2x2- 8is {-2, 3, 5}, then the range is

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Answer:

{0, 10, 42}

Step-by-step explanation:

Domain is set of input values and range is set output values.

For the function f(x) = 2x² - 8 and domain set of {-2, 3, 5}

Range is:

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Range: {0, 10, 42}

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3 years ago