Which set represents the domain of the function shown?
{(−3, 6), (0, 2), (4, 7), (11, 15)}
a. {(6, −3), (2, 0), (7, 4), (15, 11)}
b. {2, 6, 7, 15}
c. {−3, 0, 4, 11}
d. {−3, 0, 2, 4, 6, 7, 11, 15}
The domain of a function is the set of all possible x-values (input values). In this case, the x-values are -3, 0, 4, and 11.
Therefore, the correct answer is:
c. {−3, 0, 4, 11}
Which of the following statements best describes the effect of replacing the graph of y = f(x) with the graph of y = f(x) + 20?
a. The graph of y = f(x) will shift left 20 units.
b. The graph of y = f(x) will shift down 20 units.
c. The graph of y = f(x) will shift up 20 units.
d. The graph of y = f(x) will shift right 20 units.
The effect of adding 20 to the function will shift the graph vertically.
Since the function is being shifted upward, the correct answer is:
c. The graph of y = f(x) will shift up 20 units.
What is the range of f(x) = |x − 3|?
−∞ < y ≤ 3
−3 ≤ y < ∞
0 ≤ y < ∞
3 ≤ y < ∞
The range of the function f(x) = |x - 3| is the set of all possible y-values (output values).
Since the absolute value of any number is always non-negative, the range of f(x) will be 0 or greater.
Therefore, the correct answer is:
c. 0 ≤ y < ∞
What is the equation of the line that is perpendicular to y = 2x + 3 and passes through the point (−4, 8).
y = 2x + 16
y = 2x − 20
y equals negative one-half times x
y equals negative one-half times x plus 6
The line that is perpendicular to y = 2x + 3 will have a slope that is the negative reciprocal of 2.
The slope of y = 2x + 3 is 2, so the slope of the perpendicular line will be -1/2.
Using the point-slope form of the equation of a line, we can write the equation of the perpendicular line:
y - y1 = m(x - x1)
where (x1, y1) is the given point (-4, 8) and m is the slope -1/2.
Plugging in the values, we get:
y - 8 = (-1/2)(x - (-4))
y - 8 = (-1/2)(x + 4)
y - 8 = (-1/2)x - 2
y = (-1/2)x - 2 + 8
y = (-1/2)x + 6
Therefore, the correct equation of the line is:
y = (-1/2)x + 6
A group of friends go to the movies. The function h(x) represents the amount of money spent, where x is the number of friends at the movies. Does a possible solution of (6.5, $95.25) make sense for this function? Explain your answer.
a. Yes. The input and output are both possible.
b. No. The input is not possible.
c. No. The output is not possible.
d. No. Neither the input nor output is possible.
To determine if the solution (6.5, $95.25) makes sense for the function, we need to consider if it is possible for the number of friends to be 6.5.
Typically, the number of friends at the movies is a whole number, as people cannot be in fraction amounts. Therefore, the input of 6.5 does not make sense for this function.
Thus, the correct answer is:
b. No. The input is not possible.
The table represents an absolute value function f(x).
x f(x)
−5 2
−4 1
−3 0
−2 1
−1 2
0 3
1 4
2 5
3 6
What are the vertex and range of the function?
Vertex (−3, 0), Range: {y | 0 ≤ y < ∞}
Vertex (−3, 0), Range: {y | −3 ≤ y < ∞}
Vertex (0, 3), Range: {y | 0 ≤ y < ∞}
Vertex (0, 3), Range: {y | 3 ≤ y < ∞}