Graph each function.
1) a) \(f(x)= 4^x\)
b) \(f(x) = \Large\frac{1}{3}^x\)
c) \(f(x) = 2^x\)
d) \(f(x) = \Large\frac{3}{5}^x\)
Describe the transformations of each function from the parent graph.
2) a) \(f(x) = 3\Big(\Large\frac{3}{5}\Big)^x\)
b) \(f(x) = -\Big(\Large\frac{1}{3}\Big)^{\normalsize(x - 2)}\)
c) \(f(x) = \Big(\Large\frac{1}{3}\Big)\normalsize2^{(x + 4)}\)
3) a) \(f(x) = 5(3)^{(x - 1)} - 9\)
b) \(f(x) = -\Big(\Large\frac{1}{4}\Big)\Big(\frac{4}{7}\Big)^{\normalsize(x + 5)} - \normalsize3\)
c) \(f(x) = -11(4)^{(x + 3)} + 1\)
Graph the function below. Check your solution using the GeoGebra link. Also, state the domain, range, and end behavior of the function.
1) a) \(f(x)= 4^x\)
b) \(f(x) = \Large\frac{1}{3}^x\)
c) \(f(x) = 2^x\)
d) \(f(x) = \Large\frac{3}{5}^x\)
Describe the transformations of each function from the parent graph.
2) a) \(f(x) = 3\Big(\Large\frac{3}{5}\Big)^x\)
b) \(f(x) = -\Big(\Large\frac{1}{3}\Big)^{\normalsize(x - 2)}\)
c) \(f(x) = \Big(\Large\frac{1}{3}\Big)\normalsize2^{(x + 4)}\)
3) a) \(f(x) = 5(3)^{(x - 1)} - 9\)
b) \(f(x) = -\Big(\Large\frac{1}{4}\Big)\Big(\frac{4}{7}\Big)^{\normalsize(x + 5)} - \normalsize3\)
c) \(f(x) = -11(4)^{(x + 3)} + 1\)
Graph the function below. Check your solution using the GeoGebra link. Also, state the domain, range, and end behavior of the function.
Graph each function and state the domain, range and horizontal asymptote.
10) \(f(x) = 2\Big(\frac{3}{5}\Big)^{(x - 1)} + 4\)
11) \(g(x) = -\frac{1}{2}(4)^{(x + 2)} - 5\)
12) \(h(x) = -3\Big(\frac{1}{2}\Big)^{x} + 1\)
13) \(j(x) = \frac{1}{3}\Big(\frac{1}{4}\Big)^{(x + 6)} - 2\)
14) \(k(x) = 100^{(x - 10)} + 25\)
Given the equation below for f(x), what is the average rate of change between the given x-values. Check your solution using the GeoGebra link.
\(f(x)=3^x\)
Average Rate of Change = \(\dfrac{f(b)-f(a)}{b-a}\)
15) \(x=-2\) and \(x=0\)
16) \(x=-1\) and \(x=1\)
17) \(x=0\) and \(x=2\)
Check your solutions here:
Review
18) For \(i =\sqrt{-1}\), what is the sum of \((7 + 3i) + (-8 + 9i)\)?
19) For \(i =\sqrt{-1}\), what is the difference of \((7 + 3i) - (-8 + 9i)\)?
20) Determine the difference of \((x^2y - 3y^2 + 5xy^2) - (x^2y + 3xy^2 - 3y^2)\).
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