1. Find the slope of the graph of the linear function f with f(0)=4 and f(3)=13.
I have no idea how to do this.. :(
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Evaluate the function when x=3, x=0, and x= -2.
2. f(x)=-1/2x+3
my answers: 1.5, 3, 1
3. h(x)=5.5x+4
my anwers: 20.4, 4, 7
4. g(x)=1/8-4
my answers: -3.625, -4, -4.25
5. k(x)=14-4x
my answers: 2, 14, 22
Please check if numbers 2-5 are correct. Thanks.
on the first.
slope= (f(3)-f(0))/(3-0)
the others are correct, but I would have done 4 in fractions.
Thanks a lot!! =))
KukuMonkey, double check you work when you work with negative numbers.
2.
f(x)=-1/2x+3
f(-2)=4
3. h(x)=5.5x+4
my anwers: 20.4, 4, 7
h(3)=20.5
h(0)=4 (OK)
h(-2)=-7
To find the slope of a linear function, you can use the formula:
slope = (change in y) / (change in x)
For your first question, finding the slope of the graph of the linear function f with f(0) = 4 and f(3) = 13:
Step 1: Calculate the change in y:
change in y = f(3) - f(0)
= 13 - 4
= 9
Step 2: Calculate the change in x:
change in x = 3 - 0
= 3
Step 3: Calculate the slope:
slope = (change in y) / (change in x)
= 9 / 3
= 3
Therefore, the slope of the graph of the linear function f is 3.
Now let's move on to evaluating the functions:
2. For the function f(x) = -1/2x + 3:
- Substitute x = 3:
f(3) = -1/2(3) + 3
= -3/2 + 3
= 1.5
Substitute x = 0:
f(0) = -1/2(0) + 3
= 0 + 3
= 3
Substitute x = -2:
f(-2) = -1/2(-2) + 3
= 1 + 3
= 4
Your first answer is correct, and the other two are incorrect. The correct values are:
f(3) = 1.5, f(0) = 3, f(-2) = 4.
3. For the function h(x) = 5.5x + 4:
- Substitute x = 3:
h(3) = 5.5(3) + 4
= 16.5 + 4
= 20.5
Substitute x = 0:
h(0) = 5.5(0) + 4
= 0 + 4
= 4
Substitute x = -2:
h(-2) = 5.5(-2) + 4
= -11 + 4
= -7
Your first answer is very close, but it should be rounded:
h(3) ≈ 20.5, h(0) = 4, h(-2) = -7.
4. For the function g(x) = 1/8 - 4:
- Substitute x = 3:
g(3) = 1/8 - 4
= 1/8 - 32/8
= -31/8
Substitute x = 0:
g(0) = 1/8 - 4
= 1/8 - 32/8
= -31/8
Substitute x = -2:
g(-2) = 1/8 - 4
= 1/8 - 32/8
= -31/8
Your answers are incorrect. The correct values are:
g(3) = -31/8, g(0) = -31/8, g(-2) = -31/8.
5. For the function k(x) = 14 - 4x:
- Substitute x = 3:
k(3) = 14 - 4(3)
= 14 - 12
= 2
Substitute x = 0:
k(0) = 14 - 4(0)
= 14 - 0
= 14
Substitute x = -2:
k(-2) = 14 - 4(-2)
= 14 + 8
= 22
Your answers are correct for this function:
k(3) = 2, k(0) = 14, k(-2) = 22.