Question

complete the sentence below.
the graph of every exponential function ( f(x)=a^{x},a > 0,a
eq1 ), passes through three points:__,, and__.
the graph of every exponential function ( f(x)=a^{x},a > 0,a
eq1 ), passes through three points:

Explanation:

To find the points through which the graph of \(y = a^{x}\) (\(a>0,a
eq1\)) passes, we can substitute different values of \(x\) into the function.

When \(x = 0\), \(y=a^{0}=1\) (by the property \(a^{0}=1\) for \(a
eq0\)). So the point is \((0,1)\).

When \(x = 1\), \(y=a^{1}=a\). So the point is \((1,a)\).

When \(x=- 1\), \(y=a^{-1}=\frac{1}{a}\) (by the property \(a^{-n}=\frac{1}{a^{n}}\)). So the point is \((-1,\frac{1}{a})\).

Answer:

\((-1,\frac{1}{a})\), \((0,1)\), and \((1,a)\)