Do the following sets of ordered pairs represent a function? Justify your answer.
1) \( \{ (1,4),(−2,4),(3,5),(−2,2),(1,4),(−2,4),(3,5),(−2,2) \} \)
2) \( \{ (−10,5),(12,5),(7,12),(12,−2),(−10,5),(12,5),(7,12),(12,−2) \} \)
3) \( \{(0,0),(5,4),(4,5),(−1,0)\} \)
1) \( \{ (1,4),(−2,4),(3,5),(−2,2),(1,4),(−2,4),(3,5),(−2,2) \} \)
2) \( \{ (−10,5),(12,5),(7,12),(12,−2),(−10,5),(12,5),(7,12),(12,−2) \} \)
3) \( \{(0,0),(5,4),(4,5),(−1,0)\} \)
Do the following tables represent a function? Justify your answer.
4) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & -1 & 4 & -1 & 7 & -5 \\ \hline \textbf{y} & 5 & 6 & 4 & 9 & 7 \\ \hline \end{array} \)
5) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & 0 & 1 & 2 & 3 & 4 \\ \hline \textbf{y} & 5 & 6 & 6 & 7 & 8 \\ \hline \end{array} \)
6) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & -2 & -1 & 0 & 1 & 2 \\ \hline \textbf{y} & 7 & 8 & 9 & 10 & -11 \\ \hline \end{array} \)
4) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & -1 & 4 & -1 & 7 & -5 \\ \hline \textbf{y} & 5 & 6 & 4 & 9 & 7 \\ \hline \end{array} \)
5) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & 0 & 1 & 2 & 3 & 4 \\ \hline \textbf{y} & 5 & 6 & 6 & 7 & 8 \\ \hline \end{array} \)
6) \( \begin{array}{|c|c|c|c|c|c|} \hline \textbf{x} & -2 & -1 & 0 & 1 & 2 \\ \hline \textbf{y} & 7 & 8 & 9 & 10 & -11 \\ \hline \end{array} \)
Do the following graphs represent a function? Justify your answer.
15) Create a set of ordered pairs that is not a function. Justify your answer.
16) Create a graph that is a function, explain why it is. Justify your answer.
17) Create a table that repeats the output once that is still a function. Justify your answer.
18) Given the following graph, what is a possible point that would make the graph not a function?
16) Create a graph that is a function, explain why it is. Justify your answer.
17) Create a table that repeats the output once that is still a function. Justify your answer.
18) Given the following graph, what is a possible point that would make the graph not a function?
19) Is the following a function? Let each day of the year be an input and each student at a school an output. If each day of the year is paired with a student in the school, would this represent a function? Explain your reasoning.
20) If the input is a student's ID number and the output is their picture, would this represent a function? Explain your reasoning.
21) Evaluate the following.
a) \( f(-2) \) if \( f(x)=-x+4 \)
b) \( g(12) \) if \( g(x)=-2x−4 \)
c) Find \(x\) if \( f(x)=-11 \) when \(f(x)=14x−6 \)
d) Find \(x\) if \(h(x)=32\) when \(h(x)=14−x \)
e) \( g \left(\frac{2}{3} \right)\) when \(g(x)=-x−2\)
f) Find \(x\) if \(h(x)=−6 \) when \(h(x)=−3x−7 \)
20) If the input is a student's ID number and the output is their picture, would this represent a function? Explain your reasoning.
21) Evaluate the following.
a) \( f(-2) \) if \( f(x)=-x+4 \)
b) \( g(12) \) if \( g(x)=-2x−4 \)
c) Find \(x\) if \( f(x)=-11 \) when \(f(x)=14x−6 \)
d) Find \(x\) if \(h(x)=32\) when \(h(x)=14−x \)
e) \( g \left(\frac{2}{3} \right)\) when \(g(x)=-x−2\)
f) Find \(x\) if \(h(x)=−6 \) when \(h(x)=−3x−7 \)
Review
23) Verify whether \(x = 7\) is a solution to \(-4x + 20 < -8\)
24) Verify whether \(x = -3\) is a solution to \(2 - x \geq 4\)
25) Verify whether \(x = 5\) is a solution to \(0.4x - 1.7 \leq 0.3\)
23) Verify whether \(x = 7\) is a solution to \(-4x + 20 < -8\)
24) Verify whether \(x = -3\) is a solution to \(2 - x \geq 4\)
25) Verify whether \(x = 5\) is a solution to \(0.4x - 1.7 \leq 0.3\)