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Ronch [10]
3 years ago
11

Find the domain and range for the following functions:

Mathematics
1 answer:
Andreyy893 years ago
4 0

Answer with Step-by-step explanation:

Since we have given that

a. f: ℝ → ℝ given by f(x) = x + 2

Domain would be all real numbers i.e. (-∞, ∞)

Range would be all real numbers i.e. (-∞, ∞)

b. g: ℝ → ℝ given by g(x) = √x − 1

Domain would be all positive numbers i.e. [0,∞)

Range would be [-1,∞)

c. f(g(x))

f(g(x))=f(\sqrt{x}+1)=\sqrt{x}+1+2=\sqrt{x}+3

Domain would be  [0,∞)

Range would be [3,∞)

d. g(f(x))

g(x+2)=\sqrt{x+2}-1

Domain would be [-2,∞)

Range would be (0,∞)

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The rule for Function A is y= -2/3x
Rom4ik [11]

Answer:

Both functions have negative rates of change

Function B has a greater rate of change than Function A

Step-by-step explanation:

we know that

<em>Function A</em>

The rule for Function A is

y=-\frac{2}{3}x

This is the equation of a proportional relationship (the line passes through the origin)

The slope is equal to m=-\frac{2}{3}

<em>Function B</em>

Find the equation of the function B

we have the points (-2,0) and (0,-2)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

m=\frac{y2-y1}{x2-x1}

substitute the values

m=\frac{-2-0}{0+2}

m=\frac{-2}{2}

m=-1

The equation of the function B in slope intercept form is equal to

y=mx+b

we have

m=-1\\b=-2

substitute

y=-x-2

<u><em>Verify each statement</em></u>

Option 1) Both functions have negative rates of change

The statement is true

Because, the rate of change is the slope of the linear equation

Function A ----> m=-\frac{2}{3}

Function B ----> m=-1

Option 2) Both functions have the same rate of change.

The statement is false (see the explanation)

The rate of change are different ( m=-2/3 and m=-1)

Option 3) When graphed, Function A and Function B are parallel

The statement is false

When graphed, Function A and Function B are intersecting lines, because their slopes are different

Option 4) Function B has a greater rate of change than Function A

The statement is true

Remember that the rate of change can be either positive (increasing function) or negative (decreasing function). To find out which function has a greater rate of change, compare the absolute value of their slopes

therefore

1 > 2/3

6 0
3 years ago
Help please I don’t know how anyone understands this
Natalija [7]

lol it's so hard I can't proses

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2 years ago
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wolverine [178]

Answer:

The answer for the first equation is,

X = 6, -4

The answer for second equation is,

X = 9,2

7 0
2 years ago
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which transformations would result in a geometric figure that is exactly the same size and shape as DEF?
Ludmilka [50]
Rotation, Translation, and Reflection are the 3 rigid motions that preserve angle measure and side length.
A dilation only preserves angle measure.
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7 0
3 years ago
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Simplify -4(x - 7) + (x + 14).
asambeis [7]

Answer:

=−3x+42

Step-by-step explanation:

Let's simplify step-by-step.

−4(x−7)+x+14

Distribute:

=(−4)(x)+(−4)(−7)+x+14

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Combine Like Terms:

=−4x+28+x+14

=(−4x+x)+(28+14)

=−3x+42

3 0
3 years ago
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