Question

Match each exponential function to its graph.
m(x)=2
1
5
x–2c(x)=
–
2
1
5
x+2
w(x)=2
1
5
x–2z(x)=
–
2
1
5
x+2
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Submit

Answer 1

I can’t reliably read the four small graphs from the text you pasted. Could you either upload a clear picture of the four graphs or paste the coordinate(s) of any visible points (for example whether any graph goes through (2,1) or (-2,-1), whether it is above or below the x-axis, and whether it is increasing or decreasing)?

If the four functions are the ones I think they are:
- m(x) = 2^{(1/5)(x − 2)}
- c(x) = −2^{(1/5)(x + 2)}
- w(x) = 2^{−(1/5)(x − 2)} (equivalently 2^{(1/5)(2 − x)})
- z(x) = −2^{−(1/5)(x + 2)} (equivalently −2^{(1/5)(−x − 2)})

then you can match them this way:
- m(x): positive (above x-axis), increasing exponential, shifted right 2. It crosses (2,1).
- c(x): negative (below x-axis), increasing exponential, shifted left 2. It crosses (−2,−1).
- w(x): positive, decreasing (decay) exponential, shifted right 2. It crosses (2,1).
- z(x): negative, decreasing exponential, shifted left 2. It crosses (−2,−1).

So identify each graph by:
1. Is the curve above or below the x-axis? (determines the sign)
2. Is it increasing or decreasing? (determines sign of exponent)
3. Does it pass through (2,1) or (−2,−1)? (determines the horizontal shift)

Send a clearer image or tell me which graph is above/below and increasing/decreasing and whether it passes through (2,1) or (−2,−1), and I’ll give the exact match.