5.7 Functions

For the function $f \left(x\right) = 2 x^{2} + 3 x - 1$, evaluate the function.

1. $f \left(3\right)$
2. $f \left(- 2\right)$
3. $f \left(a\right)$

The number of unread emails in Sylvia’s inbox is 75. This number grows by 10 unread emails a day. The function $N \left(t\right) = 75 + 10 t$ represents the relation between the number of emails, $N$, and the time, $t$, measured in days. Find $N$(5). Explain what this result means.

Use the set of ordered pairs to determine whether the relation is a function.

1. $\left\{\left(- 3 , 27\right) , \left(- 2 , 8\right) , \left(- 1 , 1\right) , \left(0 , 0\right) , \left(1 , 1\right) , \left(2 , 8\right) , \left(3 , 27\right)\right\}$
2. $\left\{\left(9 , - 3\right) , \left(4 , - 2\right) , \left(1 , - 1\right) , \left(0 , 0\right) , \left(1 , 1\right) , \left(4 , 2\right) , \left(9 , 3\right)\right\}$

Determine whether each equation is a function. Assume $x$ is the independent variable.

1. $2 x + y = 7$
2. $y = x^{2} + 1$
3. $x + y^{2} = 3$

For $\left\{\left(1 , 1\right) , \left(2 , 4\right) , \left(3 , 9\right) , \left(4 , 16\right) , \left(5 , 25\right)\right\}$:

1. Find the domain of the relation.
2. Find the range of the relation.