# Calculus AB

Which of the following functions is continuous at x = 3? (5 points)

Select one:
a. f of x equals the quotient of the quantity x squared minus 9 and the quantity x plus 3
b. f of x equals the quotient of the quantity x squared minus 9 and the quantity x minus 3 for x not equal to 3 and equals 3 for x equals 3
c. f of x equals the quotient of the quantity x squared minus 9 and the quantity x minus 3 for x not equal to 3 and equals 0 for x equals 3 Incorrect
d. All are continuous at x = 3

1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. a) f(x) = (x^2 - 9)/(x+3)
= (x^2 - 3^2)/(x+3)
= (x+3)(x-3)/(x+3)
= (x-3)

Since this function is a linear one, it'll be continuous at all points.

b) Using the similar identity as above,
f(x) = (x+3), for x =/= 3
Now, at all points except 3, the function is given by (x+3). So at points getting closer to 3, the function tends towards 6. But as per the question, f(3) = 3.
Hence, it is discontinous at 3.

c) This is the same as part (b), except f(3) equals 0 instead of 3. However, the same argument can be used to show its discontinuity.

1. 👍
2. 👎
3. ℹ️
4. 🚩
2. (a) f is continuous at all points except x = -3, so it is continuous at x=3

1. 👍
2. 👎
3. ℹ️
4. 🚩

## Similar Questions

1. ### math

Suppose f and g are continuous functions such that g(3) = 4 and lim x → 3 [3f(x) + f(x)g(x)] = 35. Find f(3).

2. ### Math

(08.02)The scores of several classmates on a science test are shown below: 85 points 91 points 76 points 80 points 83 points 89 points 94 points 75 points 84 points 94 points What is the median score for these students? 83 points

3. ### math

If two quantities vary directly, which must be true of a graph showing the relationship between them? Select all that apply. A. The graph is a curve. B. The points on the graph are connected. C. The graph increases from left to

4. ### probability

Problem 2. Continuous Random Variables 2 points possible (graded, results hidden) Let 𝑋 and 𝑌 be independent continuous random variables that are uniformly distributed on (0,1) . Let 𝐻=(𝑋+2)𝑌 . Find the probability

1. ### math

which functions have the same transformations as f(x)=3csc(x+6)-4? select all that apply f(x)= 3(x+6)/x-4 f(x)=(3e^x+6)-4 f(x)=3sin(x+4) f(x)=3(x+6)^2)-4 (x+6)^2+(y-4)^2=3

2. ### linear algebra

Let V be the set of all real-valued continuous functions defined on R1. If f and g are in V, we define f ⊕ g by (f ⊕ g)(t) = f(t) + g(t). If f is in V and c is a scalar, we define c f by (c f)(t) = cf(t). Then V is a vector

3. ### calc

3. the graph of a function F crosses the x-axis at -1 and 3 and touches the x-axis at 5. which equations could define this function select all that apply a- f(x)= (x+1)(x-3)(x-5) b- f(x)= (x+1)(x-3)(x-5)^2 c- f(x)=

4. ### Algebra 2

Which statements represent the relationship between y=2x and y=log2x ? Select each correct answer. The equation ​ y=log2x ​ is the logarithmic form of ​ y=2x ​.

1. ### Career planning

Please help I dont know if im right? What are the building blocks of a personality? Select all that apply. (2 points) emotional qualities*******

2. ### CAL

Which of the following functions is continuous but not differentiable at x = 1? Functions: I.y=3√x-1 II.y={x^2,x≤1 2x,x>1 III. y={x,x≤1 1/x,x>1 I'm not really sure how to do this, but I've been trying and I keep getting both

3. ### algebra 2

f(x)={2x,x1} Given the piecewise functions shown below, select all of the statements that are true. A.f(5)=1 B.f(2)=4 C.f(-2)=4 D.f(1)=5

4. ### Algebra

Select the functions whose average rate of change over the interval -1 to 2 is 2. Select all that apply: A. 1+4x/2 B.x^2-x C.x^2 D.x^2+x I think its B and D but idk