Comparing Functions Graphically

The graphs of two functions are shown. Which statements accurately compare the functions in the graph? Select two options.

• Neither function has a maximum value.

• The functions share a y-intercept of −1.

• The functions share an x-intercept of 1.

• Both functions have a range of all real numbers.

• Both functions have a domain of all real numbers.

The tables show linear functions representing the cost for purchasing different amounts of broccoli and cauliflower. Broccoli Amount (lbs): 2.5, 3, 3.25, 4.15 Cost ($): 3.00, 3.60, 3.90, 4.98 Cauliflower Amount (lbs): 2.75, 3.2, 3.85, 4.5 Cost ($): 2.75, 3.20, 3.85, 4.50 Which function has the greater slope and what does it indicate?

• The broccoli function has the greater slope, which shows that the cost per pound of broccoli is less than the cost per pound of cauliflower.

• The broccoli function has the greater slope, which shows that the cost per pound of broccoli is greater than the cost per pound of cauliflower.

• The cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is less than the cost per pound of broccoli.

• The cauliflower function has the greater slope, which shows that the cost per pound of cauliflower is greater than the cost per pound of broccoli.

As the weight of purchased items increases, the shipping charges increase, as shown in the table below.

Assuming only positive domain values, which statement is true of the graph that represents the

total cost, y, in dollars for shipping items that weigh x ounces?

• The graph is discontinuous at x = 5, x = 10, and x = 15.

• The range values for the set of the data are 10, 14, 17, and 21.

• For every 1-ounce increase in weight, the total shipping cost increases by $3.75.

• The left side of each horizontal interval is a closed circle, and the right side is an open circle.

Which step is included in the graph of the function f(x) = ⌈x – 1⌉?

• y = –5 for –4 ≤ x < –3

• y = –2 for –2 ≤ x < –1

• y = –2 for –2 < x ≤ –1

• y = –5 for –4 < x ≤ –3

Which graph represents the following piecewise defined function?
f(x) = { –2x, x < –1
–1, –1 ≤ x < 2
x – 1, x ≥ 2 }

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Which of the following accurately lists all of the discontinuities for the function graphed below?

• jump discontinuity at x = 0; point discontinuity at x = 8

• jump discontinuity at x = 0; point discontinuities at x = -2 and x = 8

• jump discontinuities at x = 0 and x = 8; point discontinuity at x = -2

• jump discontinuity at x = 0; point discontinuities at x = -2, x = 3 and x = 8

What are the domain and range of f(x) = |x + 6|?

• domain: (−∞,∞); range: f(x) ≥ 0

• domain: x ≤ −6; range: (−∞,∞)

• domain: x ≥ −6; range: (−∞,∞)

• domain: (−∞,∞); range: f(x) ≤ 0

Given the function f(x) = 3|x − 2| + 6, for what values of x is f(x) = 18?

• x = −2, x = −8

• x = −2, x = −6

• x = −2, x = 6

• x = −2, x = 8

Julia is offered a job selling advertising for two different companies. Company A offers a base salary of $30,000 per year plus a year-end bonus equal to 3% of her total sales. Company B offers a base salary of $25,000 per year plus a year-end bonus equal to 5% of her total sales. Which statement best describes the two offers?

• Company A pays better when total sales are less than $37,500, but company B pays better

  when total sales exceed $37,500.

• Company A pays better when total sales are less than $250,000, but company B pays better

  when total sales exceed $250,000.

• Company B pays better when total sales are less than $37,500, but company A pays better

  when total sales exceed $37,500

• Company B pays better when total sales are less than $250,000, but company A pays better

  when total sales exceed $250,000.

• $0.03

• $0.50

• $0.95

• $2.00