Which function rule represents the input-output table?
x | y
1 | 8
2 | 11
3 | 14
4 | 17
A: h(x)=-3x-5
B: h(x)=3x+5
C: h(x)=-3x+5
D: h(x)=3x-5
11 - 8 = 3
14 - 11 = 3
17 - 14 = 3
If x increases by increases by 1, y increases by increases by 3, so this is a linear function.
Slope for any linear function is:
m = ( yA - yB ) / ( xA - xB )
where:
xA, yA is first point
xB, yB is second point
You can choose any two points e.g.
xA = 1 , yA = 8
xB = 3 , yB = 14
m = ( yA - yB ) / ( xA - xB ) = ( 14 - 8 ) / ( 3 - 1 ) = 6 / 2 = 3
The slope-intercept form of a straight line:
y = m x + b
In this case:
y = 3 x + b
Select any point to calculate the value of b.
e.g.
x = 4 , y = 17
y = 3 x + b
17 = 3 ∙ 4 + b
17 = 12 + b
Subtract 12 to both sides
5 = b
b = 5
So:
y = m x + b
y = 3 x + 5
Answer B
@Bosnian THANK YOU!!!
To determine which function rule represents the given input-output table, we need to observe the pattern between the values of x and y. By examining the values, we can calculate the change in y for every 1 unit change in x.
From the table, we notice that the change in y for every 1 unit change in x is always 3. This means the function has a slope of 3.
Next, we need to identify the y-intercept (the value of y when x is 0) to determine the constant term in the function.
For the given table, when x = 0, y is equal to 5. Therefore, the y-intercept is 5.
Putting it all together, the function rule that represents the input-output table is h(x) = 3x + 5.
Therefore, the correct answer is B: h(x) = 3x + 5.
To find the function rule that represents the given input-output table, we need to analyze the relationship between the input (x) and the output (y) values.
Looking at the table, we can see that as the input (x) increases by 1, the output (y) increases by 3. This tells us that there is a constant rate of change.
Let's test each function rule and see which one matches the given table:
A: h(x) = -3x - 5
If we substitute x = 1 into this function, we get h(1) = -3(1) - 5 = -3 - 5 = -8, which does not match the output value of 8.
B: h(x) = 3x + 5
If we substitute x = 1 into this function, we get h(1) = 3(1) + 5 = 3 + 5 = 8, which matches the output value of 8 for x = 1.
If we substitute x = 2 into this function, we get h(2) = 3(2) + 5 = 6 + 5 = 11, which matches the output value of 11 for x = 2.
If we substitute x = 3 into this function, we get h(3) = 3(3) + 5 = 9 + 5 = 14, which matches the output value of 14 for x = 3.
If we substitute x = 4 into this function, we get h(4) = 3(4) + 5 = 12 + 5 = 17, which matches the output value of 17 for x = 4.
Since all the output values from this function match the given table, the correct function rule is B: h(x) = 3x + 5.
Therefore, the answer is B: h(x) = 3x + 5.