Quick Check Solutions
Quick Check #1
1) The domain of this function is all real numbers which can also be written as \((-\infty,\infty)\) or \(\left\{x|x \in \mathbb{R}\right\}\) because you can raise the base to any power that is a real number.
2) The range of this function is all real numbers greater than \(0\) or \((0,\infty)\).
3) The \(y\)-intercept is \((0, 1)\).
4) The end behavior of this function is as follows: As \(x\rightarrow\infty, f(x)\rightarrow\infty\) and as \(x\rightarrow-\infty, f(x)\rightarrow0\). This means that \(f(x)=2^x\) is an exponential growth function because as \(x\rightarrow\infty, f(x)\rightarrow\infty\).
Quick Check #2
1) Because this function approaches \(0\) as \(x\) approaches negative infinity, this graph has a horizontal asymptote at \(y=0\). A horizontal asymptote is a horizontal line that a function’s graph approaches as \(x\) approaches negative infinity or \(x\) approaches positive infinity.
Quick Check #3
1) The end behavior is as follows: As \(x\rightarrow\infty, f(x)\rightarrow0\) and as \(x\rightarrow-\infty, f(x)\rightarrow\infty\). This means that \(f(x)=\Large\left(\frac{1}{2}\right)^x\) is an exponential decay function because as \(x\rightarrow\infty, f(x)\rightarrow0\).
Quick Check #1
1) The domain of this function is all real numbers which can also be written as \((-\infty,\infty)\) or \(\left\{x|x \in \mathbb{R}\right\}\) because you can raise the base to any power that is a real number.
2) The range of this function is all real numbers greater than \(0\) or \((0,\infty)\).
3) The \(y\)-intercept is \((0, 1)\).
4) The end behavior of this function is as follows: As \(x\rightarrow\infty, f(x)\rightarrow\infty\) and as \(x\rightarrow-\infty, f(x)\rightarrow0\). This means that \(f(x)=2^x\) is an exponential growth function because as \(x\rightarrow\infty, f(x)\rightarrow\infty\).
Quick Check #2
1) Because this function approaches \(0\) as \(x\) approaches negative infinity, this graph has a horizontal asymptote at \(y=0\). A horizontal asymptote is a horizontal line that a function’s graph approaches as \(x\) approaches negative infinity or \(x\) approaches positive infinity.
Quick Check #3
1) The end behavior is as follows: As \(x\rightarrow\infty, f(x)\rightarrow0\) and as \(x\rightarrow-\infty, f(x)\rightarrow\infty\). This means that \(f(x)=\Large\left(\frac{1}{2}\right)^x\) is an exponential decay function because as \(x\rightarrow\infty, f(x)\rightarrow0\).