draw the line of the function with its given domain. Then determine the range using interval notation:
h(x)=0.5x-1 with domain (-∞,4).
Thank you...(can you explain it to me)
clearly the graph is just a straight line, so
just check h(x) at the endpoints of the domain.
h(-∞) = -∞
h(4) = 1
so the range is (-∞,1)
To draw the line of the function \( h(x) = 0.5x - 1 \) with its domain \((-∞,4)\), follow these steps:
1. Determine the slope and y-intercept: The equation is given in slope-intercept form, \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept. The slope is 0.5, and the y-intercept is -1.
2. Plot the y-intercept: On the y-axis, mark the point (0, -1), since the y-intercept is -1.
3. Use the slope to find additional points: Since the slope is 0.5, you can move one unit to the right and go up 0.5 units to get another point. So, from the y-intercept, move one unit to the right and go up 0.5 units to plot the point (1, -0.5).
4. Draw the line: Once you have at least two points, use a straight edge to draw a line passing through them. The line should extend in both directions.
Now, let's determine the range of the function using interval notation:
The range of a function represents the set of all possible y-values or outputs of the function. To find the range, we need to consider the values that the function can take.
As we can see from the graph, the line extends upwards indefinitely. Therefore, the range of \( h(x) \) is \((-∞, +∞)\), which means that the function can take any real number as its output.
In interval notation, this would be expressed as \((-∞, +∞)\).
To draw the line of the function h(x) = 0.5x - 1 with the given domain (-∞, 4), we can start by finding the coordinates of two points on the line.
First, let's pick x = 0. By substituting this value into the equation, we can find the corresponding y-coordinate:
h(0) = 0.5(0) - 1
h(0) = -1
So, one point on the line is (0, -1).
Next, let's pick x = 4. Substituting this value into the equation:
h(4) = 0.5(4) - 1
h(4) = 2 - 1
h(4) = 1
So, another point on the line is (4, 1).
Now, we can plot these two points on a graph and draw a straight line passing through them. The line will have a positive slope since the coefficient of x is positive.
Regarding the range using interval notation, we need to determine the set of all possible y-values that the function can take. From the graph, we can see that the line extends indefinitely in both directions. Therefore, the range of the function is (-∞, ∞) in interval notation.