Sketch the graph of each linear
function. Give the domain and range.
(a) f(x) = -2x + 1
(b)f(x) = -3.
a. F(x) = Y = -2X + 1.
Use the following points for graphing:
(-2,5), (0,1), (2,-3).
Domain = All real valus of X.
b. F(x) = Y = -3.
Since Y is constant(-3),X is varying.
Therefore, we have a hor. line; and Y
equals -3 for all values of X.
(-2,-3), (0,-3), (2,-3).
Domain = all values of X.
To sketch the graph of a linear function, we need to find at least two points on the graph and connect them with a straight line. We can find these points by choosing different values for x and calculating the corresponding y values using the given function.
(a) For the function f(x) = -2x + 1:
1. Choose a value for x and substitute it into the equation to find the corresponding y value. For example, let's choose x = 0:
f(0) = -2(0) + 1 = 1
So, one point on the graph is (0, 1).
2. Choose another value for x and find the corresponding y value. Let's choose x = 2:
f(2) = -2(2) + 1 = -4 + 1 = -3
Another point on the graph is (2, -3).
Now, we can plot these two points on a coordinate system and connect them with a straight line:
|
|
|
|
|
--0----------------------
|
|
|
|
|
The domain of a linear function is the set of all possible x-values. In this case, there are no restrictions on x, so the domain is all real numbers: (-∞, +∞).
The range of a linear function is the set of all possible y-values. We can observe from the graph that the y-values can take any value, so the range is also all real numbers: (-∞, +∞).
(b) For the function f(x) = -3:
Since this function does not have an x-term, it means that the y-value (output) is always -3, regardless of the value of x. This means the graph will be a horizontal line passing through the point (0, -3).
|
|
|
|
|
--0----------------------
|
|
|
|
|
The domain is still all real numbers: (-∞, +∞), as there are no restrictions on x.
The range, however, is a single value, because the y-value is always -3, so the range is { -3 }.