Quiz 4.3:
Question:
Given the function \( f(x)=\left\{\begin{matrix} 2^x & ,x<0\\ 0 &,x=0 \\ 1-\frac{1}{2}x &,x>0 \end{matrix}\right. \)
a) Graph \(f\) for \( -3 \leq x \leq 4 \)
b) Give the domain and range of the entirety of \(f\)
c) What are the \( x \) and \( y \) intercepts?
d) What happens to \( f \) as \( x \rightarrow \infty \) and \( x \rightarrow -\infty \)?
b) Give the domain and range of the entirety of \(f\)
c) What are the \( x \) and \( y \) intercepts?
d) What happens to \( f \) as \( x \rightarrow \infty \) and \( x \rightarrow -\infty \)?
Solution:
a) 
b) Domain \( = \mathbb{R} \) and Range \(= \left ( - \infty , 1 \right ) \)
c) x-intercepts at \(x=0,2 \) and y-intercept at \(y=0\)
d) \( f \rightarrow -\infty\) as \( x \rightarrow \infty \) and \( f \rightarrow 0\) as \( x \rightarrow -\infty \)
b) Domain \( = \mathbb{R} \) and Range \(= \left ( - \infty , 1 \right ) \)
c) x-intercepts at \(x=0,2 \) and y-intercept at \(y=0\)
d) \( f \rightarrow -\infty\) as \( x \rightarrow \infty \) and \( f \rightarrow 0\) as \( x \rightarrow -\infty \)
