AP Calculus ABmediummcq1 pt
Let f(x) = 1/(x - 4) for x ≠ 4, with f(4) = 0. On which of the following intervals is f continuous?
A.[0, 3]
B.[0, 5]
C.[3, 5]
D.[4, 6]
Explanation
Core Concept
The only threat to continuity is x = 4, where the denominator vanishes and the function blows up; assigning f(4) = 0 cannot fix an infinite discontinuity. Every point of [0, 3] avoids x = 4, and there f is a quotient of continuous functions with nonzero denominator, so f is continuous throughout [0, 3].
Correct Answer
A[0, 3]
More Unit 1: Limits and Continuity practice questions
- hardLet $f(x)=\begin{cases} x^2+ax, & x<1 \\ bx+3, & x>1 \end{cases}$. If $f(1)=2$ and $f$ is continuous at $x=1$, what is $a+b$?
- hardSuppose $x^3\le f(x)\le x$ for all $x$ in $(0,1)$. What is $\lim_{x\to 0^+} f(x)$?
- hard$\lim_{x\to 0} x^2\sin\left(\frac{1}{x}\right)=$
- hardSuppose $f$ is continuous on $[0,3]$ with $f(0)=-4$ and $f(3)=1$. Which statement is guaranteed by the Intermediate Value Theorem?
- hardLet $f(x)=x^3-x-1$. Given that $f(1)=-1$ and $f(2)=5$, which interval is guaranteed to contain a zero of $f$ by the Intermediate Value Theor…
Practice more AP Calculus AB questions with full explanations
Practice Unit 1: Limits and Continuity Questions →