Question

graph this function.
$y = \frac{1}{2}(5)^x$
plot two points to graph the function.
(graph with x-axis from -8 to 8 and y-axis from -8 to 8, grid lines, and origin at (0,0))
submit
work it out
not feeling ready yet? these can help:
evaluate an exponential function
negative exponents
lesson: exponential functions

Explanation:

Step1: Choose x=0

Substitute \( x = 0 \) into \( y=\frac{1}{2}(5)^{x} \). Using the rule \( a^{0}=1 \) (for \( a
eq0 \)), we get \( y=\frac{1}{2}(5)^{0}=\frac{1}{2}\times1=\frac{1}{2} \). So the point is \( (0, \frac{1}{2}) \).

Step2: Choose x=1

Substitute \( x = 1 \) into \( y=\frac{1}{2}(5)^{x} \). Then \( y=\frac{1}{2}(5)^{1}=\frac{1}{2}\times5=\frac{5}{2} = 2.5 \). So the point is \( (1, 2.5) \).
(To graph, plot these two points and draw the exponential curve through them. The function is an exponential growth function since the base \( 5>1 \), scaled by \( \frac{1}{2} \).)

Answer:

Two points to plot are \( (0, \frac{1}{2}) \) and \( (1, \frac{5}{2}) \) (or \( (1, 2.5) \)). When graphing, connect these points with a smooth curve representing the exponential function \( y = \frac{1}{2}(5)^{x} \).