Practice with Functions

Determine if a Relation is a Function

In the following exercises, use the set of ordered pairs to a. determine whether the relation is a function, b. find the domain of the relation, and c. find the range of the relation.

295. $\{(-3,9),(-2,4),(-1,1)$

$(0,0),(1,1),(2,4),(3,9)\}$

297. $\{(-3,27),(-2,8),(-1,1)$

$(0,0),(1,1),(2,8),(3,27)\}$

In the following exercises, use the mapping to a. determine whether the relation is a function, b. find the domain of the function, and c. find the range of the function.

299.

301.

In the following exercises, determine whether each equation is a function.

303.

a. $2 x+y=-3$

b. $y=x^{2}$

c. $x+y^{2}=-5$

305.

a. $y-3 x^{3}=2$

b. $x+y^{2}=3$

c. $3 x-2 y=6$

Find the Value of a Function

In the following exercises, evaluate the function: a. $f(2)$ b. $f(-1)$ c. $f(a)$.

307. $f(x)=5 x-3$

309. $f(x)=-4 x+2$

311. $f(x)=x^{2}-x+3$

313. $f(x)=2 x^{2}-x+3$

In the following exercises, evaluate the function: a. $g\left(h^{2}\right)$ b. $g(x+2)$ c. $g(x)+g(2)$.

315. $g(x)=2 x+1$

317. $g(x)=-3 x-2$

319. $g(x)=3-x$

In the following exercises, evaluate the function.

321. $f(x)=3 x^{2}-5 x ; f(2)$

323. $F(x)=2 x^{2}-3 x+1$; $F(-1)$

325. $h(t)=2|t-5|+4 ; h(-4)$

327. $f(x)=\frac{x+2}{x-1} ; f(2)$

Source: Rice University, https://openstax.org/books/intermediate-algebra-2e/pages/3-5-relations-and-functions
This work is licensed under a Creative Commons Attribution 4.0 License.

295.

a. yes

b. $\{-3,-2,-1,0,1,2,3\}$

c. $\{9,4,1,0\}$

297.

a. yes

b. $\{-3,-2,-1,0,1,2,3\}$

c. $\{0,1,8,27\}$

299.

a. yes

b. $\{-3,-2,-1,0,1,2,3\}$

c. $\{0,1,2,3\}$

301.

a. no

b. {Jenny, R and y, Dennis, Emily, Raul}

c. {RHern and ez@state.edu, JKim@gmail.com, Raul@gmail.com, ESmith@state.edu, DBroen@aol.com, jenny@aol.cvom, R and y@gmail.com}

303. 

a. yes

b. yes

c. no

305.

a. yes

b. no

c. yes

307.

a. $f(2)=7$

b. $f(-1)=-8$

c. $f(a)=5 a-3$

309. 

a. $f(2)=-6$

b. $f(-1)=6$

c. $f(a)=-4 a+2$

311.

a. $f(2)=5$

b. $f(-1)=5$

c. $f(a)=a^{2}-a+3$

313.

a. $\text { (a) } f(2)=9$

b. $f(-1)=6$

c. $f(a)=2 a^{2}-a+3$

315.

a. $g\left(h^{2}\right)=2 h^{2}+1$

b. $g(x+2)=2 x+5$

c. $g(x)+g(2)=2 x+6$

317.

a. $g\left(h^{2}\right)=-3 h^{2}-2$

b. $g(x+2)=1-x$

c. $g(x)+g(2)=4-x$

319.

a. $g\left(h^{2}\right)=3-h^{2}$

b. $g(x+2)=1-x$

c. $g(x)+g(2)=4-x$

321. $2$

323. $6$

325. $22$

327. $4$