SOLUTION: consider the function f(x)=7^x, g(x)=4^x, and h(x)=4^-x. the graphs of wchi functions pass through (0,1) have the x-axis as a horizontal asymptote and increases as x increases?

Algebra ->  Trigonometry-basics -> SOLUTION: consider the function f(x)=7^x, g(x)=4^x, and h(x)=4^-x. the graphs of wchi functions pass through (0,1) have the x-axis as a horizontal asymptote and increases as x increases?      Log On


   

Question 1181878: consider the function f(x)=7^x, g(x)=4^x, and h(x)=4^-x. the graphs of wchi functions pass through (0,1) have the x-axis as a horizontal asymptote and increases as x increases?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answer: f(x) and g(x)

Both of these functions are increasing (due to the base being larger than 1). Both of these functions have the y intercept (0,1) because plugging x = 0 leads to y = 1.

h(x) can be written as h(x) = (1/4)^x and we can see that this is a decaying function because the base 1/4 is less than 1.

All three functions have the same horizontal asymptote: which is y = 0. The curves approach this "electric fence" but don't actually get there.

All three functions have the same y intercept, as mentioned before.

Graph:
+graph%28+500%2C+500%2C+-5%2C+5%2C+-10%2C+10%2C+7%5Ex%2C+4%5Ex%2C4%5E%28-x%29%29+
f(x) in red
g(x) in green
h(x) in blue

As the red and green curves indicate, they are increasing functions. As we move from left to right, we're going uphill. As x increases, so does y.