Use the function rule ƒ(x) = x • |–1|x. Find the output ƒ(2). A. 4 B. 3 C. –2 D. 2
ƒ(2) = 2 • |–1|2
Since the absolute value of –1 is 1, this simplifies to:
ƒ(2) = 2 • 1 • 2
ƒ(2) = 4
So the answer is A. 4.
3x + y = 2
A. Graph A
B. Graph B
C. Graph C
D. Graph D
To graph the equation 3x + y = 2, we can rearrange it into slope-intercept form y = -3x + 2.
A. Graph A does not intersect the point (0,2) where the line crosses the y-axis, so it cannot be the graph of this equation.
B. Graph B intersects the point (0,2), but the slope appears to be positive rather than negative, so it cannot be the graph of this equation.
C. Graph C appears to have a negative slope and intersects the point (0,2), which is consistent with the equation y = -3x + 2, so it is a possible graph of this equation.
D. Graph D has a negative slope, but it does not intersect the point (0,2), so it cannot be the graph of this equation.
Therefore, the answer is C. Graph C.
Do the data in the table represent a linear function? If so, write a rule for the function.
x –2 –1 0 1 2
y –7 1 8 17 25
A. yes; y = 8x + 9
B. yes; y = 8x + 8
C. yes; y = one eighthx + 8
D. no
To determine if the data in the table represent a linear function, we need to check if there is a constant rate of change between the x and y values.
We can calculate the rate of change by finding the difference in y-coordinates over the difference in the corresponding x-coordinates.
Using the first two points:
Rate of change = (1 - (-7)) / (-1 - (-2)) = 8
Using the last two points:
Rate of change = (25 - 17) / (2 - 1) = 8
Since both calculations yield the same rate of change, we can conclude that the data represents a linear function.
To find the rule for the function, we can use the slope-intercept form of a linear function, y = mx + b, where m is the slope and b is the y-intercept.
To find the slope, we can use any two points from the table. Let's use (-1,1) and (0,8):
m = (8 - 1) / (0 - (-1)) = 7/1 = 7
So the rule for the function is y = 7x + b. To find the value of b, we can substitute one of the points and solve for b. Let's use (0,8):
8 = 7(0) + b
b = 8
Therefore, the rule for the function is y = 7x + 8, which is closest to answer B. Yes; y = 8x + 8.
Use the slope and two points to write a linear function rule for the Graph.
A line on a coordinate graph passes through a point with coordinates 2 comma negative 2 and a point with coordinates 4 comma 2.
A. y = –2x – 6
B. y = 2x – 6
C. y = one-halfx – 6
D. y = one-halfx + 6
7 / 7
6 of 7 Answered
Let's use the two-point form of a linear equation:
y - y1 = m(x - x1)
where m is the slope, and (x1, y1) are the coordinates of one of the points.
We are given the points (2, -2) and (4, 2). Let's choose (2, -2) as our point and calculate the slope:
m = (y2 - y1) / (x2 - x1) = (2 - (-2)) / (4 - 2) = 4/2 = 2
Now that we have the slope, we can plug in the values for one of the points and simplify:
y - (-2) = 2(x - 2)
y + 2 = 2x - 4
y = 2x - 6
Therefore, the linear function rule for the graph is y = 2x - 6, which matches answer choice B.