Piecewise Defined Functions — Quiz

Question 1

A rental car company charges a base fee of 40 dollars plus 0 point 2 5 dollars per mile for the first 100 miles the car is driven. The company charges the same base fee plus a reduced price of 0 point 1 8 dollars per mile for cars driven over 100 miles. The given piecewise function represents the different amounts the company charges. y equals enlarged left-brace first row 40 plus 0 point 2 5 m comma m less than or equal to 100. Second row 40 plus 0 point 1 8 m comma m greater than 100. If someone drives their rental car 150 miles, how much will they owe the rental company?

Revolt · Accepted Answer

67 point 0 0 dollars

Question 2

Which graph represents the following piecewise defined function? g of x equals enlarged left-brace first row one half x plus 3 comma x less than negative 2. Second row 2 comma negative 2 less than or equal to x less than or equal to 3. Third row 2 x minus 3 comma x greater than 3.

Revolt · Accepted Answer

Image with description On a coordinate plane, the scale on the x axis range from negative 9 to 7 in increments of 1, and the scale on the y axis range from negative 4 to 8 in increments of 1. The graph is comprised of 3 lines. The first line starts from the open circle at (negative 2 comma 3) and goes to (negative 6 comma 1). The second line starts from the closed circle at (negative 2 comma 2) and goes to the open circle (3 comma 2). The Third line starts from the closed circle at (3 comma 3) and goes to (5 comma 7).

Question 3

Which of the graphed functions has a removable discontinuity?

Revolt · Accepted Answer

Image with description On a coordinate plane, the scale on the x axis range from negative 8 to 8 in increments of 1, and the scale on the y axis range from negative 5 to 5 in increments of 1. The graph is comprised of 2 curves. The curve starts at the open circle (0 comma 0) and curves up through (negative 2 comma 4). The curve starts at the open circle (0 comma 0) and curves down through (2 comma negative 4). Both the curves are connected.

Question 4

Which graph represents the following piecewise defined function? g of x equals enlarged left-brace first row x squared comma x less than 0. Second row one half x comma 0 less than x less than or equal to 4. Third row x comma x greater than 4.

Revolt · Accepted Answer

Image with description On a coordinate plane, the scale on the x axis range from negative 8 to 8 in increments of 1, and the scale on the y axis range from negative 3 to 9 in increments of 1. The graph is comprised of a curve and 2 lines. The curve starts at (0 comma 0) and curves up through (negative 3 comma 9). The first line starts from the closed circle at (0 comma 0) and goes to (4 comma 2). The second line starts from the closed circle at (4 comma 2) and goes to (7 comma 7).

Question 5

Which of the graphed functions is continuous?

Revolt · Accepted Answer

Image with description On a coordinate plane, the scale on the x axis range from negative 8 to 8 in increments of 1, and the scale on the y axis range from negative 5 to 5 in increments of 1. The graph is comprised of a curve and 2 lines. The line starts at the closed circle (0 comma 0) and goes through (negative 3 comma negative 3). The curve starts at the closed circle (0 comma 0) and curves up through (2 comma 4). The other line starts at the closed circle (2 comma 4) and goes to (5 comma 4).

Question 6

A cell phone company charges by the minute (and partial minute) for making phone calls. Arionna’s plan includes 300 minutes in the 20 dollars monthly base cost. If she uses more than 300 minutes in a month, there is a 5 dollars overage fee and an additional charge of 0 point 2 5 dollars per minute. Which graph represents the monthly cost, y , in dollars for making x minutes of calls?

Revolt · Accepted Answer

Image with description On a coordinate plane, the x axis is labeled as minutes and the y axis is labeled as cost. The x axis ranges from negative 50 to 500 in increments of 50. The y axis ranges from negative 50 to 50 in increments of 10. The graph is comprised of 2 lines. The first line starts from the closed circle (0 comma 20) and goes to (300 comma 20). The second line starts from the open circle (300 comma 25) and goes to (400 comma 50).

Question 7

Which graph represents the following piecewise defined function? g of x equals enlarged left-brace first row negative 2 x comma x less than negative 2. Second row negative x squared comma negative 2 less than or equal to x less than 1. Third row x comma x greater than or equal to 1.

Revolt · Accepted Answer

Image with description On a coordinate plane, the scale on the x axis range from negative 6 to 6 in increments of 1, and the scale on the y axis range from negative 4 to 8 in increments of 1. The graph is comprised of a parabola and 2 lines. The first line starts from the open circle at (negative 2 comma negative 4) and goes to (negative 4 comma 8). The parabola is facing downwards with a vertex of (0 comma 0). The second line starts from the closed circle at (1 comma 1) and goes to (4 comma 4).

Question 8

After a heavy rainstorm, Barbara’s dog left muddy paw prints all over her back patio. She decided to rent an electric pressure washer to clean up the mess. The given piecewise function shows the rental charges for the pressure washer, dependent upon how many hours she rents it. Due to high demand, you cannot rent the washer for more than 24 hours at a time. Barbara’s brother asked to use the washer and agreed to pay Barbara for any additional monies owed. y equals enlarged left-brace first row 26 comma 0 less than h less than or equal to 4. Second row 26 plus 5 times open paren h minus 4 closed paren comma 4 less than h less than or equal to 8. Third row 60 comma 8 less than h less than or equal to 24. If Barbara used the washer for 3 hours and her brother returned it to the store 7 hours after she rented it, how much does her brother owe her?

Revolt · Accepted Answer

15 point 0 0 dollars

Question 9

Which of the following accurately lists all discontinuities of the given function? f of x equals enlarged left-brace first row 4 comma x less than negative 4. Second row open paren x plus 2 closed paren squared comma negative 4 less than or equal to x less than or equal to negative 2. Third row negative one half x plus 1 comma negative 2 less than x less than 4. Fourth row negative 1 comma x greater than 4.

Revolt · Accepted Answer

point discontinuities at x is equal to negative 4 and x is equal to 4 ; jump discontinuity at x is equal to negative 2

Question 10

Which graph represents the following piecewise defined function? f of x equals enlarged left-brace first row x comma x less than negative 2. Second row negative 2 comma negative 2 less than or equal to x less than 1. Third row x minus 3 comma x greater than or equal to 1.

Revolt · Accepted Answer

Image with description On a coordinate plane, the scale on the x and y axes ranges from negative 5 to 5 in increments of 1. The graph is comprised of 3 lines. The first line starts from a closed circle at (negative 2 comma negative 2) and goes to (negative 4 comma negative 4). The second line starts from a closed circle at (negative 2 comma negative 2) and goes to closed circle (1 comma negative 2). The Third line starts from a closed circle at (1 comma negative 2) and goes to (4 comma 1).

Piecewise Defined Functions — Quiz Answers

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