Question

The table shows the outputs, y, for different inputs, x:

Input (x) 2 5 9 12
Output (y) 20 15 12 8



Part A: Do the data in this table represent a function? Justify your answer. (3 points)

Part B: Compare the data in the table with the relation f(x) = 5x + 14. Which relation has a greater value when x = 9? (2 points)

Part C: Using the relation in Part B, what is the value of x if f(x) = 64? (5 points)

Answer 1

a)


`\bf \begin{array}l x&2&5&9&12\\ y&20&15&12&8 \end{array} \begin{array}{llll} \impliedby \textit{notice the x-values do not re} peat\\ \qquad \textit{therefore is a function} \end{array}`

b)


`\bf \begin{array}lllll x&2&5&\stackrel{\downarrow }{9}&12\\ y&20&15&\boxed{12}&8 \end{array}\qquad \qquad \begin{array}{llll} f(x)=5x+14\\\\ x=9\\\\ 5(9)+14\implies 45+14\implies \boxed{59} \end{array}`

well, notice, which is larger?

c)


`\bf \stackrel{f(x)}{64}=5x+14\implies 50=5x\implies \cfrac{50}{5}=x\implies 10=x`