If your started with a function \( f(x) \) and changed it into \( g(x) \) describe how the function changes and what the end behavior of \( g(x) \) is. Use the applet below to check your conclusions.
1) \( f(x)=2 \cdot 3^x \ \ \text{and} \ \ \ g(x)=2 \cdot 2^x \)
2) \( f(x)=1 \cdot 2^x \ \ \text{and} \ \ \ g(x)=-1 \cdot 2^x \)
3) \( f(x)=2 \cdot 2^x \ \ \text{and} \ \ \ g(x)=2 \cdot \Big( \dfrac{1}{2} \Big)^x \)
4) \( f(x)=2 \cdot 3^x \ \ \text{and} \ \ \ g(x)=\Big( \dfrac{1}{3} \Big) \cdot 3^x \)
1) \( f(x)=2 \cdot 3^x \ \ \text{and} \ \ \ g(x)=2 \cdot 2^x \)
2) \( f(x)=1 \cdot 2^x \ \ \text{and} \ \ \ g(x)=-1 \cdot 2^x \)
3) \( f(x)=2 \cdot 2^x \ \ \text{and} \ \ \ g(x)=2 \cdot \Big( \dfrac{1}{2} \Big)^x \)
4) \( f(x)=2 \cdot 3^x \ \ \text{and} \ \ \ g(x)=\Big( \dfrac{1}{3} \Big) \cdot 3^x \)
Using a 10 by 10 graph sketch the function given and compare to \( f(x)=2^x \). Also comment on the end behavior. Use the applet above to check your answers.
5) \( h(x)=\text{-}2 \cdot 2^x \)
6) \( k(x)=2 \cdot 4^x \)
7) \( m(x)= \Big( \dfrac{1}{4} \Big)^x \)
Create a function that has the following characteristics:
8) \( \text{a y-intercept of} \ 3 \\ \ \ \ \ \text{As} \ x \rightarrow \ \text{-} \infty \ \text{then} \ f(x) \rightarrow \ 0 \\ \ \ \ \ \text{As} \ x \rightarrow \ \infty \ \text{then} \ f(x) \rightarrow \ \infty \\ \)
9) \( \text{a y-intercept of} \ \text{-} \dfrac{1}{2} \\ \ \ \ \ \text{As} \ x \rightarrow \ \text{-} \infty \ \text{then} \ f(x) \rightarrow \ 0 \\ \ \ \ \ \text{As} \ x \rightarrow \ \infty \ \text{then} \ f(x) \rightarrow \ \text{-} \infty \\ \)
Review
10) Write an equation of a line in standard form passing through the points: \( (4, -2) \) and \( (8, -4) \).
11) Graph the line: \( y + 2 = -(x - 4) \).
12) Write the following in function form: \( 2x - 4y = 12 \).
Practice Problems Solution Bank