Exponential question

[Jaemin]

I'm not sure how you would sketch a graph of the following two equations labeling

1. at least 2 coordinates on each side of the y axis
2. the asymptote

a) f(x) = 2x b) g(x) = (1/3)x

 

[tkhunny]

These are lines through the Origin. Nothing "exponential" about them.

 

[Steven G]

Did you mean that f(x) = 2^x and g(x) = (1/3)^x

 

[HallsofIvy]

The basic way to graph any function y= f(x) is to calculate a few coordinate pairs: \(\displaystyle (x_0, y_0)= (x_0, f(x_0))\), plot those points a draw a curve through them. For \(\displaystyle y= 2^x\) they might be \(\displaystyle (0, 2^0)= (0, 1)\), \(\displaystyle (1, 2^1)= (1, 2)\), \(\displaystyle (2, 2^2)= (2, 4)\), \(\displaystyle (-1, 2^{-1})= (-1, 1/2)\), \(\displaystyle (-2, 2^{-2})= (-2, 1/4)\). For \(\displaystyle y= (1/3)^x\) they might be \(\displaystyle (0, (1/3)^0)= (0, 1)\), \(\displaystyle (1, (1/3)^1)= (1, 1/3)\), \(\displaystyle (2, (1/3)^2)= (2, 1/9)\), \(\displaystyle (-1, (1/3)^{-1})= (-1, 3)\), \(\displaystyle (-2, (1/3)^{-2})= (-2, 9)\).

You say
"labeling
1. at least 2 coordinates on each side of the y axis.
2. the asymptote."
"On each side of the y axis" means some negative and some positive x values, But "2" makes no sense. neither graph has an "asymptote".

 

[Steven G]

I think that you should know how to graph y= a^x for 0<a<1 and for a>1.

Maybe a few times yo plot many many points to see how they look. After that I tell my students to plot these type graphs with just two points.
1st x-value. Use what ever x-value makes the power equal to 0.
2nd x-value. Use what ever x-value that makes the power equal to 1.
Now find the corresponding y-values.

Plot those two points and then graph the curves.