5.7.1: Exercises

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Jan 2, 2025
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- 5.7: Functions
- 5.8: Graphing Functions

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For the following exercises, evaluate the functions at the values $f\left({-2}\right),f\left({-1}\right),f\left(0\right),f\left(1\right),$ and $f\left(2\right)$ .

Exercise $\PageIndex{1}$

$f\left(x\right)=4-2x$

Exercise $\PageIndex{2}$

$f\left(x\right)=8-3x$

Exercise $\PageIndex{3}$

$f\left( x \right) = 8{x^2}-7x + 3$

Exercise $\PageIndex{4}$

$f\left( x \right) = 3 + \sqrt {x + 3}$

Exercise $\PageIndex{5}$

$f(x)=\frac{x-2}{x+3}$

Exercise $\PageIndex{6}$

$f(x)=x^3$

For the following exercises, determine whether the ordered pairs represent a function.

Exercise $\PageIndex{7}$

$\left\{ {\left( {-1,-1} \right),\left( {-2,-2} \right),\left( {-3,-3} \right)} \right\}$

Exercise $\PageIndex{8}$

$\left\{ {\left( {3,4} \right),\left( {4,5} \right),\left( {5,6} \right)} \right\}$

Exercise $\PageIndex{9}$

$\left\{ {\left( {2,5} \right),\left( {7,11} \right),\left( {15,8} \right),\left( {7,9} \right)} \right\}$

Exercise $\PageIndex{10}$

$\left\{ {\left( {-3{\text{ }},9} \right),\left( {-2,4} \right),\left( {-1,1} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {2,4} \right),\left( {3,9} \right)} \right\}$

Exercise $\PageIndex{11}$

$\left\{ {\left( {9,-3} \right),\left( {4,-2} \right),\left( {1,-1} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {4,{\text{ }}2} \right),\left( {9,3} \right)} \right\}$

For the following exercises, determine whether the mapping represented a function.

Exercise $\PageIndex{12}$

$Mapping of names and birthdays. Names and birthdays are as follows. Rebecca: January 18. Jennifer: April 1. John: January 18. Hector: June 23. Luis: February 15. Ebony: April 7. Raphael: November 6. Meredith: August 19. Karen: August 19. Joseph: July 30.$

Exercise $\PageIndex{12}$

$Mapping of names and birthdays. Names and birthdays are as follows. Amy: February 24. Carol: May 30. Devon: January 5. Harrison: January 7. Jackson: November 26. Labron: April 7. Mason: July 20. Natalie: March 1. Paul: August 1. Sylvester: November 13.$

For the following exercises, determine whether the equations represent $y$ as a function of $x$ .

Exercise $\PageIndex{14}$

$5x+2y=10$

Exercise $\PageIndex{15}$

$y = {x^2}$

Exercise $\PageIndex{16}$

$x = {y^2}$

Exercise $\PageIndex{17}$

$3{x^2} + y = 14$

Exercise $\PageIndex{18}$

$2x + {y^2} = 6$

Exercise $\PageIndex{19}$

$y = - 2{x^2} + 40x$

For the following exercises, use the vertical line test to determine which graph represents a function.

Exercise $\PageIndex{20}$

$A polynomial function is plotted on an x y coordinate plane. The x and y axes range from negative 5 to 5, in increments of 1. The function passes through the points, (negative 2, 0), (negative 1, 3), (0, 0), (1, negative 3), and (2, 0). Note: all values are approximate.$

Exercise $\PageIndex{21}$

$Two rays are plotted on an x y coordinate plane. The x and y axes range from negative 5 to 5, in increments of 1. The first ray passes through the points, (0, 0), (1, 0), (2, 1), and (3, 4). The second ray passes through the points, (0, 0), (1, 0), (2, negative 1), and (3, negative 4).$

Exercise $\PageIndex{22}$

$A hyperbola is plotted on an x y coordinate plane. The x and y axes range from negative 5 to 5, in increments of 1. One arm of the hyperbola passes through the points, (negative 3, 0.5), (negative 1.5, 1), and (negative 0.5, 5). The other arm passes through the points, (0.5, negative 3), (0.8, negative 1.5), and (5, negative 0.5). Note: all values are approximate.$

Exercise $\PageIndex{23}$

$A line is plotted on an x y coordinate plane. The x and y axes have 10 units, each. The line passes through the points, (negative 5, negative 2), (negative 1, negative 2), (0, 0), (1, 2), and (5, 2).$

Exercise $\PageIndex{24}$

$An ellipse is plotted on an x y coordinate plane. The x and y axes have 10 units, each. The center of the ellipse is at (2.5, negative 3). The ellipse passes through the points, (1, negative 3), (2.5, negative 2), (2.5, negative 4), and (4, negative 3).$

Exercise $\PageIndex{25}$

$A polynomial function is plotted on an x y coordinate plane. The x and y axes have 10 units, each. The function passes through the points, (negative 2, negative 2), (negative 1, 0), (0, 0), (1, 0), and (2, 2).$

For the following exercises, use the set of ordered pairs to find the domain and the range.

Exercise $\PageIndex{26}$

$\left\{ {\left( {-3,9} \right),\left( {-2,4} \right),\left( {-1,1} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {2,4} \right),\left( {3,9} \right)} \right\}$

Exercise $\PageIndex{27}$

$\left\{ {\left( {-9,-3} \right),\left( {-4,-2} \right),\left( {-1,-1} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {4,2} \right),\left( {9,3} \right)} \right\}$

Exercise $\PageIndex{28}$

$\left\{ {\left( {-3,27} \right),\left( {-2,8} \right),\left( {-1,1} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {2,8} \right),\left( {3,27} \right)} \right\}$

Exercise $\PageIndex{29}$

$\left\{ {\left( {-3,-27} \right),\left( {-2,-8} \right),\left( {-1,-1} \right),\left( {0,0} \right),\left( {1,1} \right),\left( {2,8} \right),\left( {3,27} \right)} \right\}$

For the following exercises, use the graph to find the domain and the range.

Exercise $\PageIndex{30}$

$Six points are plotted on an x y coordinate plane. The x and y axes range from negative 5 to 5, in increments of 1. The points are plotted at the following coordinates: (negative 3, 4), (negative 2, negative 1), (0, negative 3), (2, 3), (4, negative 1), and (4, negative 3).$

Exercise $\PageIndex{31}$

$Six points are plotted on an x y coordinate plane. The x and y axes range from negative 5 to 5, in increments of 1. The points are plotted at the following coordinates: (negative 3, 4), (negative 2, 0), (negative 3, negative 4), (1, 5), and (4, negative 2).$

Exercise $\PageIndex{32}$

$Six points are plotted on an x y coordinate plane. The x and y axes range from negative 5 to 5, in increments of 1. The points are plotted at the following coordinates: (negative 1, 4), (0, 3), (1, 4), (0, negative 3), (negative 1, negative 4), and (1, negative 4).$

Exercise $\PageIndex{33}$

$Six points are plotted on an x y coordinate plane. The x and y axes range from negative 5 to 5, in increments of 1. The points are plotted at the following coordinates: (negative 2, negative 6), (negative 1, negative 3), (0, 0), (0.5, 1.5), (1, 3), and (2, 6).$

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Exercise $\PageIndex{12}$

Exercise 5.7.1.1\PageIndex{1}

Exercise 5.7.1.2\PageIndex{2}

Exercise 5.7.1.3\PageIndex{3}

Exercise 5.7.1.4\PageIndex{4}

Exercise 5.7.1.5\PageIndex{5}

Exercise 5.7.1.6\PageIndex{6}

Exercise 5.7.1.7\PageIndex{7}

Exercise 5.7.1.8\PageIndex{8}

Exercise 5.7.1.9\PageIndex{9}

Exercise 5.7.1.10\PageIndex{10}

Exercise 5.7.1.11\PageIndex{11}

Exercise 5.7.1.12\PageIndex{12}

Exercise 5.7.1.12\PageIndex{12}

Exercise 5.7.1.14\PageIndex{14}

Exercise 5.7.1.15\PageIndex{15}

Exercise 5.7.1.16\PageIndex{16}

Exercise 5.7.1.17\PageIndex{17}

Exercise 5.7.1.18\PageIndex{18}

Exercise 5.7.1.19\PageIndex{19}

Exercise 5.7.1.20\PageIndex{20}

Exercise 5.7.1.21\PageIndex{21}

Exercise 5.7.1.22\PageIndex{22}

Exercise 5.7.1.23\PageIndex{23}

Exercise 5.7.1.24\PageIndex{24}

Exercise 5.7.1.25\PageIndex{25}

Exercise 5.7.1.26\PageIndex{26}

Exercise 5.7.1.27\PageIndex{27}

Exercise 5.7.1.28\PageIndex{28}

Exercise 5.7.1.29\PageIndex{29}

Exercise 5.7.1.30\PageIndex{30}

Exercise 5.7.1.31\PageIndex{31}

Exercise 5.7.1.32\PageIndex{32}

Exercise 5.7.1.33\PageIndex{33}

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