Question

Which of the following functions shown in the table below could not be an exponential function?

f(x)

g(x)

h(x)

k(x)

Answer 1

The slope of an exponential function changes, it's not static.
But for h(x) we see it's always the same.. for each step on the \(x\) the \(y\) grows by another 0.25
So h(x) is a straight line function and not exponential
Is that explanation good enough? =S

Answer 2

ok so f(x) , g(x), k(x) are exponential

Answer 3

which makes h(x) the only answer?

Answer 4

Well after checking the definition better (sorry about that):
http://tutorial.math.lamar.edu/Classes/Alg/ExpFunctions.aspx
Which means it could only be in a way of
\[
v(x) = a^x
\]
And \(a\) is a constant that could change..
This means, that the ratio between \(v(x+1)\) and \(v(x)\) is... \(a\) since
\[
\frac{v(x+1)}{v(x)} = \frac{a^{x+1}}{a^x} = a^{x+1-x} = a
\]
So let's see, which functions follow this rule..
f(x) has f(0) = 3 and f(1) = 5.95.. the ratio is \(\frac{5.95}{3} \) = 1.97666...
But the ratio between f(1) and f(2) is \(\frac{9.15}{5.95} \) = 1.538
So that can't be exponential.
Wanna try by yourself the rest?

Answer 5

Notice also that in f(x) life are much simpler, I just showed the idea for the rest but
\[
x = 0 \quad \implies \quad a^x = a^0 = 1
\]
And f(0) is 3...