Review 1ap Calculus
Posted By admin On 29/12/21Play this game to review Calculus. Given piecewise function f(x) shown, over which interval is f continuous? Copyright © 2008 Laying the Foundation, Inc., Dallas, Texas. All rights reserved. These materials may be used for facetoface teaching with students only.
Unit 1  Limits and Continuity

Test your readiness for the AP Calculus exam with this quiz!
Answer 1
A: If the graph of a function has a sharp point, the function is not differentiable at that point. This is because the slopes directly to the left and right of the point do not approach the same value.
An absolute value function has a sharp point at its vertex. The graph off(x)= x + 4 is a horizontal translation (to the left 4 units) of the standard absolute value function, y = x , which has vertex (0, 0). Thus, the vertex of fis (4, 0), which means the function is not differentiable at x =4. Choice (A) is correct.
Answer 2
D: The only discontinuities that are removable are holes and holes with a point above or below—this function has neither. The function has 2 jump discontinuities (gaps), at x=2 and x= 0, but neither of these is removable.
Answer 3
D: Examine the values in the table: f(x) increases as x gets larger, which indicates that f′(x), the slope of the function, is positive. This means f′(x)> 0, so eliminate (A) and (B).
To choose between (C) and (D), take a closer look at the slopes. The slope between the first pair of points is 3, and the slope between the second pair of points is also 3, so f′(x) is constant. This means f′′(x), which is the derivative of f′(x), must be 0. Choice (D) is correct
Answer 4
C: To use a local linear approximation, you need to find the equation of the tangent line. You’ve been given all the information you need in the question stem; you just need to piece it all together. The point on the function is given by f(1)= 5, which translates to the point (1, 5). The slope of the tangent line at x=1 is given by f'(1)= 2, so the slope is 2. Now the pointslope form of the tangent line is:
Ap Calculus Semester 1 Review
y5 = 2(x(1))
y = 5+2(x+1)
Ap Calculus Unit 1 Review
Substituting x=0.9 into the equation of the tangent line yields:
5+2(0.9+1) = 5+2(0.1) = 5.2
Ap Calculus Bc Semester 1 Review
That’s (C).
For more practice questions, check out our AP Calculus Prep Plus book.