Graph the function y=5(1/4)^x

Question

. Complete the ordered pairs for the x-values of −2
, −1
, 0, and 1 by finding the y-values.

Answer 1

To graph the function $y=5{\left(\frac{1}{4}\right)}^x$ and find the ordered pairs for the specified x-values, we will calculate the corresponding y-values.

Let's calculate the y-values for the given x-values:

1. For $x=-2$: $$y=5{\left(\frac{1}{4}\right)}^{-2}=5{\left(\frac{4}{1}\right)}^2=5\times 16=80$$ So, the ordered pair is $(-2,80)$.

2. For $x=-1$: $$y=5{\left(\frac{1}{4}\right)}^{-1}=5{\left(\frac{4}{1}\right)}^1=5\times 4=20$$ So, the ordered pair is $(-1,20)$.

3. For $x=0$: $$y=5{\left(\frac{1}{4}\right)}^0=5\times 1=5$$ So, the ordered pair is $(0,5)$.

4. For $x=1$: $$y=5{\left(\frac{1}{4}\right)}^1=5\times \frac{1}{4}=\frac{5}{4}=1.25$$ So, the ordered pair is $(1,1.25)$.

Now, we have the following ordered pairs:

• $(-2,80)$
• $(-1,20)$
• $(0,5)$
• $(1,1.25)$

You can plot these points on a coordinate graph to visualize the function $y=5{\left(\frac{1}{4}\right)}^x$. The graph will show a decreasing exponential function.