Question

55 the graph below shows $f(x) = 2^x$. if the graph is shifted up one, what is the new $y$-intercept? \
\
a $(1,0)$ \
b $(1,1)$ \
c $(0,2)$ \
d $(0,0)$

Explanation:

Step1: Find original y - intercept

For \(f(x)=2^{x}\), when \(x = 0\), \(f(0)=2^{0}=1\). So the original y - intercept is \((0,1)\).

Step2: Determine the new function

Shifting the graph of \(y = f(x)\) up by 1 unit gives the new function \(g(x)=f(x)+1=2^{x}+1\).

Step3: Find new y - intercept

For the new function \(g(x)=2^{x}+1\), when \(x = 0\), \(g(0)=2^{0}+1=1 + 1=2\). So the new y - intercept is \((0,2)\).

Answer:

C. \((0,2)\)