Exercises

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
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