The table below represents a linear function f(x) and the equation represents a function g(x):
x f(x)
−1 −5
0 −1
1 3
g(x) g(x) = 2x − 7
Part A: Write a sentence to compare the slope of the two functions and show the steps you used to determine the slope of f(x) and g(x).
Part B: Which function has a greater y-intercept? Justify your answer.
for f(x), using (0,-1) and (1,3), the slope
= (3+1)/(1-0) = 4
and the slope of g(x) = 2x - 7 is obviously 2, so .....
(write your sentence
as to part B, isn't (0,-1) your point on the y-axis ?
and isn't the y-intercept for g(x) = 2x - 7 equal to -7 ????
so ....
Part A: To compare the slopes of the two functions, we need to determine the slope of both f(x) and g(x).
For f(x), we can use the formula for the slope of a linear function, which is given by the change in y divided by the change in x.
Using the points (-1, -5) and (1, 3), we can calculate the change in y as follows:
Change in y = 3 - (-5) = 8
And the change in x is the difference in the x-values:
Change in x = 1 - (-1) = 2
Thus, the slope of f(x) is:
slope of f(x) = change in y / change in x = 8 / 2 = 4
For g(x), the equation is given as g(x) = 2x - 7. Since the coefficient of x is the slope, we can directly determine the slope of g(x):
slope of g(x) = 2
Therefore, the slope of f(x) is 4, while the slope of g(x) is 2.
Part B: To determine which function has a greater y-intercept, we need to compare the y-intercepts of both functions.
For f(x), the y-intercept can be found by substituting x = 0 into the function:
f(0) = -1
Therefore, the y-intercept of f(x) is -1.
For g(x), the equation is given as g(x) = 2x - 7. The y-intercept is the value of g(x) when x = 0:
g(0) = 2(0) - 7 = -7
Therefore, the y-intercept of g(x) is -7.
Comparing the y-intercepts, we can see that -1 is greater than -7. Thus, f(x) has a greater y-intercept than g(x).
Part A: To compare the slopes of the two functions, we need to determine the slope of each function. The slope of a linear function can be found using the formula:
slope = (change in y) / (change in x)
For the function f(x), we can determine the slope by selecting any two points from the table and calculating the change in y divided by the change in x. Let's choose the points (-1, -5) and (1, 3):
slope of f(x) = (change in y)/(change in x) = (3 - (-5)) / (1 - (-1)) = 8 / 2 = 4
So, the slope of f(x) is 4.
For the function g(x), we can determine the slope by looking at the equation g(x) = 2x - 7. The coefficient of x in the equation represents the slope. Therefore, the slope of g(x) is 2.
Comparing the two slopes, we see that the slope of f(x) is 4, while the slope of g(x) is 2. Therefore, the slope of f(x) is greater than the slope of g(x).
Part B: To determine which function has a greater y-intercept, we need to compare the y-intercepts of the two functions. The y-intercept is the value of y when x = 0.
For f(x), we can see from the table that when x = 0, f(x) = -1. So, the y-intercept of f(x) is -1.
For g(x), we can refer to the equation g(x) = 2x - 7. When x = 0:
g(x) = 2(0) - 7 = -7
So, the y-intercept of g(x) is -7.
Comparing the y-intercepts, we see that the y-intercept of f(x) is -1, while the y-intercept of g(x) is -7. Therefore, g(x) has a greater y-intercept than f(x).