A, find domain each function, locate any intercept, also based on graph find the range and ? F(x) 2x of x not equal to zero
To find the domain of the function f(x) = 2x, we need to determine the set of all possible values for x.
In this case, there are no restrictions on the variable x, so the domain is all real numbers. We can express this using interval notation as (-∞, ∞).
Next, let's determine the intercepts of the function.
1. x-intercept:
The x-intercept is the point where the graph of the function intersects the x-axis. To find it, we set f(x) = 0 and solve for x.
0 = 2x
Dividing both sides by 2, we get:
x = 0
So the x-intercept of the function is (0, 0).
Now, based on the graph, let's find the range of the function.
Since the function is a linear function with a positive slope of 2, the graph is a straight line that extends infinitely in both directions.
Therefore, the range of the function is all real numbers. Using interval notation, we can express this as (-∞, ∞).
To summarize:
- Domain: (-∞, ∞)
- X-intercept: (0, 0)
- Range: (-∞, ∞)
To find the domain of a function, we are looking for the set of all possible input values (x) for which the function is defined. In this case, we are given the function f(x) = 2x, with the condition that x is not equal to zero.
The domain of this function is the set of all real numbers except for zero. We exclude zero from the domain because when x is equal to zero, the function will be undefined due to division by zero.
So, the domain of f(x) = 2x is (-∞, 0) U (0, +∞), which means any real number except for zero.
Next, we need to find the intercepts of the function. An intercept occurs when the graph of the function intersects either the x-axis or the y-axis.
For f(x) = 2x, the x-intercept occurs when f(x) = 0. Setting the function equal to zero, we have:
2x = 0
Dividing both sides by 2, we get:
x = 0
Therefore, the x-intercept of the function is at x = 0.
Now, let's determine the y-intercept. The y-intercept occurs when x = 0 (since we are given x cannot be zero). Therefore, substituting x = 0 into the function, we have:
f(0) = 2(0) = 0
This means that the y-intercept of the function is at y = 0.
Finally, let's find the range of the function based on the graph. The range refers to the set of all possible output values (y) for the function.
Since the function f(x) = 2x is a linear function (a straight line), its graph will continue infinitely in both positive and negative directions. This means that the range of the function is also (-∞, +∞), which includes all real numbers.
In summary:
- The domain of f(x) = 2x is (-∞, 0) U (0, +∞), excluding zero.
- The x-intercept of the function is at x = 0.
- The y-intercept of the function is at y = 0.
- The range of the function is (-∞, +∞), including all real numbers.