Number 8 a&b please!
2 answers:
Answer:
a. domain: (-∞, -2] ∪ [2, ∞); range: [0, ∞)
b. domain: (-∞, ∞); range: [2, ∞)
Step-by-step explanation:
In each case, the domain is the set of x-values for which the function is defined. A square root function will be defined where its argument is non-negative.
The range of the function is the set of values it can produce as output. A square root function cannot produce negative values. The minimum value it can produce will depend on the argument.
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a. The function is defined where ...
x² -4 ≥ 0
x² ≥ 4
|x| ≥ 2 . . . . take the square root
x ≤ -2 ∪ 2 ≤ x . . . . . the domain of the function
The value of x² -4 can be any non-negative number, so ...
0 ≤ y < ∞ . . . . . the range of the function
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b. The function is defined where ...
x² +4 ≥ 0
True for all values of x.
-∞ < x < ∞ . . . . . the domain of the function
The value of x² +4 cannot be less than 4, so the function value cannot be less than √4 = 2.
2 ≤ x < ∞ . . . . . the range of the function
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Answer:
Example of an equation with an undefined slope: x = 2
Step-by-step explanation:
<h2>Definitions</h2>The standard form of linear equations with an <u>undefined slope</u> is <em>x</em> = <em>a</em>, whose graph represents a vertical line. The value of a in the standard form is the x-intercept, (<em>a</em>, 0).
The slope is the ratio of the vertical change in y-values to the horizontal change in x-values.
The slope of a vertical line is undefined because if we were to solve its slope, the denominator will be zero. As we know, division by zero is an undefined operation.
<h2>Example:</h2>For example, suppose that we have the following points (2, 5) (2, 10).
Let (x₁, y₁) = (2, 5)
(x₂, y₂) = (2, 10)
Substitute these values into the slope formula:
Dividing the numerator, 5, by the denominator, 0, will have an undefined quotient.
Thus, the equation of the <u>vertical line</u> will be: x = 2, where <em>a</em> = 2.