Graph and compare the following functions on the same graph. Then use those results to answer the questions below.
\(f(x)=x^2\)
\(g(x)=x^2+4x+8\)
1) What is the domain and range for \(f(x)\)?
2) What is the domain and range for \(g(x)\)?
3)Does \(f(x)\) have a minimum or maximum? What is it?
4) Does \(g(x)\) have a minimum or maximum? What is it?
5) As \(x\rightarrow\infty\) what happens to \(f(x)\)?
6) As \(x\rightarrow\infty\) what happens to \(g(x)\)?
7) As \(x\rightarrow -\infty\) what happens to \(f(x)\)?
8) As \(x\rightarrow -\infty\) what happens to \(g(x)\)?
Given the tables of quadratic functions below:
a) Is there a minimum or a maximum?
b) Does it open up or down?
c) As \(x\rightarrow\infty\) what happens to the function?
d) What is the vertex?
9) \(\begin{array}{|c|c|c|c|c|c|}
\hline
x & \text{-}4 & \text{-}3 & \text{-}2 & \text{-}1 & 0\\
\hline
f(x) & \text{-}4 & 1 & 4 & 5 & 4\\
\hline
\end{array}\)
10) \(\begin{array}{|c|c|c|c|c|c|}
\hline
x & \text{-}2 & \text{-}1 & 0 & 1 & 2\\
\hline
g(x) & 10 & 7 & 6 & 7 & 10\\
\hline
\end{array}\)
11) \(\begin{array}{|c|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 & 4\\
\hline
h(x) & 9 & 4 & 1 & 0 & 1\\
\hline
\end{array}\)
12) \(\begin{array}{|c|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 & 4\\
\hline
j(x) & -2 & 1 & 2 & 1 & -2\\
\hline
\end{array}\)
13) \(\begin{array}{|c|c|}
\hline
x & k(x)\\
\hline
0 & 6\\
\hline
1 & 3\\
\hline
2 & 2\\
\hline
3 & 3\\
\hline
4 & 6\\
\hline
\end{array}\)
14) \(\begin{array}{|c|c|}
\hline
x & d(x)\\
\hline
0 & 21\\
\hline
1 & 16\\
\hline
2 & 13\\
\hline
3 & 12\\
\hline
4 & 13\\
\hline
\end{array}\)
Given the three quadratic functions:
\(f(x)=x^2\)
\(g(x)=x^2+4x+8\)
1) What is the domain and range for \(f(x)\)?
2) What is the domain and range for \(g(x)\)?
3)Does \(f(x)\) have a minimum or maximum? What is it?
4) Does \(g(x)\) have a minimum or maximum? What is it?
5) As \(x\rightarrow\infty\) what happens to \(f(x)\)?
6) As \(x\rightarrow\infty\) what happens to \(g(x)\)?
7) As \(x\rightarrow -\infty\) what happens to \(f(x)\)?
8) As \(x\rightarrow -\infty\) what happens to \(g(x)\)?
Given the tables of quadratic functions below:
a) Is there a minimum or a maximum?
b) Does it open up or down?
c) As \(x\rightarrow\infty\) what happens to the function?
d) What is the vertex?
9) \(\begin{array}{|c|c|c|c|c|c|}
\hline
x & \text{-}4 & \text{-}3 & \text{-}2 & \text{-}1 & 0\\
\hline
f(x) & \text{-}4 & 1 & 4 & 5 & 4\\
\hline
\end{array}\)
10) \(\begin{array}{|c|c|c|c|c|c|}
\hline
x & \text{-}2 & \text{-}1 & 0 & 1 & 2\\
\hline
g(x) & 10 & 7 & 6 & 7 & 10\\
\hline
\end{array}\)
11) \(\begin{array}{|c|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 & 4\\
\hline
h(x) & 9 & 4 & 1 & 0 & 1\\
\hline
\end{array}\)
12) \(\begin{array}{|c|c|c|c|c|c|}
\hline
x & 0 & 1 & 2 & 3 & 4\\
\hline
j(x) & -2 & 1 & 2 & 1 & -2\\
\hline
\end{array}\)
13) \(\begin{array}{|c|c|}
\hline
x & k(x)\\
\hline
0 & 6\\
\hline
1 & 3\\
\hline
2 & 2\\
\hline
3 & 3\\
\hline
4 & 6\\
\hline
\end{array}\)
14) \(\begin{array}{|c|c|}
\hline
x & d(x)\\
\hline
0 & 21\\
\hline
1 & 16\\
\hline
2 & 13\\
\hline
3 & 12\\
\hline
4 & 13\\
\hline
\end{array}\)
Given the three quadratic functions:
15) Which function has the largest minimum value?
16) Which function has the smallest minimum value?
17) Which function(s) cross the \(x\)-axis twice?
18) Which functions(s) touch the \(x\)-axis once?
19) Which functions(s) don't touch or cross the \(x\)-axis?
20) Order from least to greatest: \(k(1), t(1), p(1)\)
Given the three quadratic functions:
16) Which function has the smallest minimum value?
17) Which function(s) cross the \(x\)-axis twice?
18) Which functions(s) touch the \(x\)-axis once?
19) Which functions(s) don't touch or cross the \(x\)-axis?
20) Order from least to greatest: \(k(1), t(1), p(1)\)
Given the three quadratic functions:
21) Which function has the largest maximum value?
22) Which function has the smallest maximum value?
23) Which function(s) cross the \(x\)-axis twice?
24) Which functions(s) touch the \(x\)-axis once?
25) Which functions(s) don't touch or cross the \(x\)-axis?
26) Which function has the smallest value for the \(y\)-intercept?
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22) Which function has the smallest maximum value?
23) Which function(s) cross the \(x\)-axis twice?
24) Which functions(s) touch the \(x\)-axis once?
25) Which functions(s) don't touch or cross the \(x\)-axis?
26) Which function has the smallest value for the \(y\)-intercept?
Solution Bank