Can you check my answers?
1. Table modeling a linear relationship is shown below. What is the rate of change of nails to birdhouses?
2 birdhouses to 22 nails
3 birdhouses to 33 nails
4 birdhouses to 44 nails
5 birdhouses to 55 nails
a. 55 nails per birdhouse
b. 2 nails per birdhouse
c. 22 nails per birdhouse
d. 11 nails per birdhouse
Ans: D (change in nails is 11 and change in birdhouses is 1, 11/1)
4. Which of the following is true about the functions f(x) and g(x)?
f(x) = 2/3x - 6
(table below):
x --- g(x)
-4 ... 10
0 ... 7
4 ... 4
8 ... 1
a. Rate of change of f(x) is less than rate of change of g(x).
b. Rate of change of f(x) is greater than rate of change of g(x).
c. The y-intercept of f(x) is equal to the rate of change of g(x).
d. The y-intercept of f(x) is greater than the rate of change of g(x).
Ans: B (b/c rate of change of g(x) is -3, rate of change of f(x) is +4 and y intercept of f(x) is -6).
10. Which equation represents the line that passes through the point (1,5) and has a slope of -2?
a. y = -2x + 7
b. y = -2x + 11
c. y = 2x - 9
d. y = 2x +3
Ans: A (b/c m=-2; solve for by substitute 1 in for x and substitute 5 in for y. get 5 = -2(1) + b, add +2 to both sides, 7 = b)
1. If f(x)= 3x + 1 and g(x) = 4x-8, find f(1) + g(-2).
a. -2
b. 4
c. 9
d. -11
Ans: Didn't get any of those answers. f(x) = 3(1) + 1 = 4
g(x) = 4(-2) - 8 = -16; 4 + -16 = -12
2. Let g(x) = x^2 - 3x +1. Find g(2).
a. 11
b. -4
c. -1
d. -3
Ans: C (2^2 - 3(2) + 1 = 4-6+1 = -1)
1. If f(x)= 3x + 1 and g(x) = 4x-8, find f(1) + g(-2).
a. -2
b. 4
c. 9
d. -11
I agree with you - none of the above but -12
I agree with the rest also
#1 D is correct
#4 B is correct, but the rate of change of f is 2/3, and of g is -3/4
#10 A is correct
#1 I agree. Must be a typo.
f(1)+g(2) = 4, however
#2 C is correct
Hi Steve,
How do you get the rate of change of 2/3 and -3/4 for problem #4?
1. To find the rate of change of nails to birdhouses, we need to calculate the change in nails divided by the change in birdhouses. Looking at the table, we can see that for each additional birdhouse, the number of nails increases by 11. Therefore, the rate of change of nails to birdhouses is 11 nails per birdhouse. So the correct answer is (d) 11 nails per birdhouse.
4. To compare the rate of change of f(x) and g(x), we need to examine the slopes of the two functions. From the equation f(x) = (2/3)x - 6, we can see that the rate of change (slope) is 2/3. Looking at the table for g(x), we can determine the rate of change by calculating the difference in the y-values divided by the difference in the x-values. The rate of change of g(x) is -3. Comparing the two rates of change, we find that the rate of change of f(x) is greater than the rate of change of g(x). So the correct answer is (b) Rate of change of f(x) is greater than rate of change of g(x).
10. To find the equation of the line passing through the point (1,5) with a slope of -2, we can use the point-slope form of a linear equation, which is y - y1 = m(x - x1), where (x1, y1) is the point and m is the slope. Substituting the given values, we get y - 5 = -2(x - 1). Simplifying, we have y - 5 = -2x + 2. Rearranging the equation, we get y = -2x + 7. So the correct answer is (a) y = -2x + 7.
1. To find f(1), we substitute 1 in for x in the function f(x) = 3x + 1. So we have f(1) = 3(1) + 1 = 4.
To find g(-2), we substitute -2 in for x in the function g(x) = 4x - 8. So we have g(-2) = 4(-2) - 8 = -16.
Finally, we add f(1) and g(-2), which gives us 4 + (-16) = -12. Therefore, the correct answer is none of the given options.
2. To find g(2), we substitute 2 in for x in the function g(x) = x^2 - 3x + 1. So we have g(2) = 2^2 - 3(2) + 1 = 4 - 6 + 1 = -1. Therefore, the correct answer is (c) -1.