Question

evaluate the following functions.

1. find f(1). f(x) = 9x + 1
2. find g(40). g(x) = \\(\frac{x}{40}\\) + 5
3. find h(2) = 2 + 5x³
4. find f(7k). f(x) = -10x - 8
5. find g(b - 5). g(x) = -4x
6. find f(y + 5). f(x) = 2x + 1

• a relation is a set of ordered pairs ________.
• the domain is the set of all possible ________ for the relation.
• the range is the set of all possible ________ for the relation.
• a function is a relation in which every ______ value corresponds to exactly one ______ value.
• if a vertical line, drawn anywhere on the graph, can touch the graph ________, then it is a function.

Explanation:

Step1: Note missing input for Q1

(Problem 1 has incomplete input: $f(x)=?x+1$ and the input value is unclear, so it cannot be solved.)

Step2: Substitute $x=40$ into $g(x)$

$g(40)=\frac{40}{40}+5$

Step3: Simplify $g(40)$

$g(40)=1+5=6$

Step4: Note missing input for Q3

(Problem 3 does not specify the input value for $h(x)=2+5x^3$, so it cannot be solved.)

Step5: Substitute $x=7k$ into $f(x)$

$f(7k)=-10(7k)-8$

Step6: Simplify $f(7k)$

$f(7k)=-70k-8$

Step7: Substitute $x=b-5$ into $g(x)$

$g(b-5)=-4(b-5)$

Step8: Simplify $g(b-5)$

$g(b-5)=-4b+20$

Step9: Substitute $x=y+5$ into $f(x)$

$f(y+5)=2(y+5)+1$

Step10: Simplify $f(y+5)$

$f(y+5)=2y+10+1=2y+11$

Step11: Fill in relation/function blanks

Use standard definitions of relations, domains, ranges, functions, and the vertical line test.

Answer:

1. Incomplete problem, cannot solve.
2. $6$
3. Incomplete problem, cannot solve.
4. $-70k-8$
5. $-4b+20$
6. $2y+11$

Fill-in-the-blank answers:

• A Relation is a set of ordered pairs.
• The DOMAIN is the set of all possible input values (x-values) for the relation.
• The RANGE is the set of all possible output values (y-values) for the relation.
• A Function is a RELATION in which every domain (input/x) value corresponds to exactly one range (output/y) value.
• If a vertical line, drawn anywhere on the graph, can touch the graph at most once, then it is a function.