Question

Match the graph to its equation.

1.
y = 2^x
2.
y = (¼)^x
3.
y = (½)^x
4.
y = 4^x

Answer 1

I don’t see the graphs attached. I can’t give the exact matches without them, but here are the rules you should use to match each graph to its equation:

- All four functions have y-intercept 1 (because any a^0 = 1).
- If the graph increases as x increases (rises to the right), the base is > 1. That means the graph is either y = 2^x or y = 4^x.
- Between those two, y = 4^x grows faster (is steeper) than y = 2^x.
- If the graph decreases as x increases (falls to the right), the base is between 0 and 1. That means the graph is either y = (1/2)^x or y = (1/4)^x.
- Between those two, y = (1/4)^x decays faster (is steeper downward) than y = (1/2)^x.

So:
- steep increasing → y = 4^x (4)
- shallow increasing → y = 2^x (1)
- steep decreasing → y = (1/4)^x (2)
- shallow decreasing → y = (1/2)^x (3)

If you upload or describe the four graphs (which one rises/falls and which looks steeper), I’ll match them exactly.