Evaluate the function when x=1. f(x)=4x-2. Write the input and output as a set of ordered pairs, and identify the domain and range of the ordered pair.
Ordered Pair:
Domain:
Range:
2. Write an equation of direct variation that passes through the point (9,1).
what? Can't plug in a value for x and evaluate? For example,
f(23) = 4*23-2 = 90
direct variation means that y = kx
So, plug in the numbers and find k.
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Where did the 23 come into play?
To evaluate the function when x=1, we substitute x=1 into the function f(x)=4x-2:
f(1) = 4(1) - 2
f(1) = 4 - 2
f(1) = 2
Therefore, when x=1, the value of the function f(x) is 2.
To write the input and output as a set of ordered pairs, we can use the coordinates (1, 2), where 1 is the input (x) and 2 is the output (f(x)):
Ordered Pair: (1, 2)
The domain is the set of all possible input values. In this case, since we have only evaluated the function for x=1, the domain consists of only one value: {1}.
Domain: {1}
The range is the set of all possible output values. In this case, we have found that when x=1, the output (f(x)) is 2. Therefore, the range consists of only one value: {2}.
Range: {2}
Now, let's move on to the second question:
To write an equation of direct variation that passes through the point (9, 1), we can use the general equation of direct variation, which is y = kx, where k is the constant of variation.
Since the point (9, 1) is given, we can substitute x=9 and y=1 into the equation:
1 = k * 9
To solve for k, we divide both sides of the equation by 9:
1/9 = k
Therefore, the equation of direct variation that passes through the point (9, 1) is:
y = (1/9)x