Relations, Functions,
Domain & Range
Domain & Range
Is the relation {(-2, 3), (3, 8), (5, -3), (6, 8), (10, 8)} a function? State the domain and range.
Yes, it is a function.
Given f(x) = -6(x - 4)+11 , evaluate f(9)
f(9) = -19
Describe the transformations required to obtain
g(x) = f(x - 5) + 4 from the parent function f(x) = x
Shift right 5 units and shift up 4 units
Determine whether the sequence 11, 18, 25, 32, 39, ... is arithmetic. If it is, identify the common difference
Yes, it is an arithmetic sequence with a common difference of d = 7
What type of association is displayed when increasing values of x correspond to decreasing values of y?
Negative association.
Is the relation {(1, 4), (-1, -4), (3, 7), (5, 4), (7, -9)} a function or not? Explain your reasoning
Yes, it is a function because every input maps to exactly one output
Given g(x) = -2x^3 +5x -8, evaluate g(-2)
g(-2) = -2
Describe the transformations required to obtain
g(x) = 1/2 f(x + 8) from the parent function f(x) = x
Vertical compression by a factor of 1/2 and shift left 8 units.
Write an explicit formula for the arithmetic sequence: 15, 11, 7, 3, -1, ...
a(n)= -4(n-1) + 15
OR
a(n) = -4n + 19
Describe the strength and direction for each correlation coefficient
a) r = -0.88
b) r = 0.35
c) r = -0.05
a) Strong negative
b) Weak positive
c) No correlation
Why is the relation {(1, -2), (-2, 0), (-1, 2), (1, 3), (0, 4)} NOT a function?
It is not a function because the input x = 1 maps to two different outputs (y = -2 and y = 3)
Given h(x) = 3|2x +1| - 14, evaluate h(-5)
h(-5) = 13
Write a function rule for g(x) if the parent function f(x) = x is reflected over the x-axis, shifted left 6 units, shifted down 2 units, and vertically stretched by a factor of 5
g(x) = -5 f(x + 6) - 2
An arithmetic sequence has a first term a(1) = -18 and a common difference d = 6. Write the explicit formula and list the first 5 terms.
a(n) = 6n - 24
OR
a(n) = 6(n - 1) - 18
Draw a trend line that fits negatively associated data with a correlation of r = -0.72
Explain how to use the Vertical Line Test on a graph to determine if it represents a function. Does a circle graph pass or fail this test?
If any vertical line intersects the graph at more than one point, it is not a function. A circle fails the vertical line test (it is not a function).
A road trip group is driving 280 miles to a national park. They have already completed 40 miles and travel at a steady rate of 60mph. Write a linear function for total distance as a function of driving hours x, and find how long the full trip takes.
f(x) = 60x + 40
Full trip takes 4 hours
Describe all transformations applied to the parent function f(x) = x to produce g(x) = -2/5 f(x - 3) + 7
Find the 85th term of the arithmetic sequence: 9, 14, 19, 24, ...
a(85) = 429
Monthly heating cost vs outdoor temperature is modeled by f(x) = -2.85x + 185.5, where x is temperature and y is the cost of the heating bill. What does the slope represent in context, and what is the predicted heating bill when the outdoor temperature is 30 degrees?
A continuous graph extends horizontally from x = -1 to x = 5 with closed endpoints, and vertically from y = -3 to y = 3. State the domain and range.
A catering company charges a fixed setup fee plus an hourly service rate. Their pricing table shows: (1, $75), (2, $105), (3, $135), (4, $165). Write the linear function, interpret the slope and y-intercept in context, and find the total cost for 6.5 hours of service.
f(x) = 30x + 45
Write a function rule g(x) describing a horizontal stretch by a factor of 8 and a horizontal shift right 10 units applied to f(x) = x.
g(x) = f (1/8x - 10)
For the sequence -7, -2, 3, 8, 13, ... show that it is arithmetic, write its explicit function rule, and calculate the value of the 61st term.
A dataset comparing shoe size x to reading score y yields a regression line
y = 0.12x + 50.4 with r = 0.08.
Explain whether this linear model can be reliably used to make predictions.
No, the model cannot be reliably used for predictions because r = 0.08 indicates virtually no linear correlation between shoe size and reading score.