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. \(\{(-3,9),(-2,4),(-1,1)\)</p> <p>\((0,0),(1,1),(2,4),(3,9)\}\)

297. \(\{(-3,27),(-2,8),(-1,1)\)</p> <p>\((0,0),(1,1),(2,8),(3,27)\}\)

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. \(4\)