use a table of coordinates to graph the exponential function. begin by selecting - 2, - 1, 0, 1, and 2 for…
use a table of coordinates to graph the exponential function. begin by selecting - 2, - 1, 0, 1, and 2 for x. based on your graph, describe the shape of a scatter plot that can be modeled by ( f(x)=b^{x},0 < b < 1 ).\n\n( f(x)=left(\frac{1}{5}\right)^{x} )\n\nfor each value of x, find the corresponding value for ( f(x) ).\n\n
Answer
Explanation:
Step1: Substitute (x = - 2) into (f(x)=\left(\frac{1}{5}\right)^{x})
Use the rule (a^{-n}=\frac{1}{a^{n}}), so (f(-2)=\left(\frac{1}{5}\right)^{-2}=5^{2} = 25)
Step2: Substitute (x=-1) into (f(x)=\left(\frac{1}{5}\right)^{x})
Using (a^{-n}=\frac{1}{a^{n}}), (f(-1)=\left(\frac{1}{5}\right)^{-1}=5^{1}=5)
Step3: Substitute (x = 0) into (f(x)=\left(\frac{1}{5}\right)^{x})
Use the rule (a^{0}=1(a\neq0)), so (f(0)=\left(\frac{1}{5}\right)^{0}=1)
Step4: Substitute (x = 1) into (f(x)=\left(\frac{1}{5}\right)^{x})
(f(1)=\frac{1}{5})
Step5: Substitute (x = 2) into (f(x)=\left(\frac{1}{5}\right)^{x})
(f(2)=\left(\frac{1}{5}\right)^{2}=\frac{1}{25})
Answer:
| (x) | (-2) | (-1) | (0) | (1) | (2) |
|---|---|---|---|---|---|
| (f(x)=\left(\frac{1}{5}\right)^{x}) | (25) | (5) | (1) | (\frac{1}{5}) | (\frac{1}{25}) |
A scatter - plot that can be modeled by (y = b^{x},0\lt b\lt1) has a shape that falls from left to right. As (x) increases, (y) decreases.