the graph of a first degree absolute value function has a Y-intercept of 3, x-intercepts of -9 and -3 , and a minimum vlaue of -3 at x=-6. on the axes provided , sketch a graph of this function.
so, did you get out your graph paper and plot the points?
They are (0,3), (-9,0), and (-3,0)
The vertex is at (-6,-3)
You know the graph will be V-shaped. Since you know that there will be a minimum at x = -6, the V opens upward.
You know that the point of the V is at x = -6. That should tell you which points to join together to the the sides of the V.
thank you !!
To sketch the graph of a first-degree absolute value function with the given information, follow these steps:
Step 1: Determine the equation of the absolute value function.
Since the given y-intercept is at (0,3), we know that the equation of the function is of the form: f(x) = |mx| + b, where b represents the y-intercept and m represents the slope or steepness of the function.
Step 2: Find the slope of the function.
To find the slope, notice that the x-intercepts are -9 and -3, which are equidistant from the y-axis (at x = 0). The distance between the x-intercepts is 9 - 3 = 6 units.
Since this is a first-degree absolute value function, the slope will be the change in y divided by the change in x: slope = Δy/Δx.
In this case, slope = 3 - (-3) / 0 - (-6) = 6/6 = 1.
The slope of the function is 1.
Step 3: Determine the equation of the function.
Using the slope (m) and the y-intercept (b), the equation of the function is:
f(x) = |1x| + 3 = |x| + 3.
Step 4: Plot the points and sketch the graph.
Start by plotting the known points:
- Y-intercept: (0,3)
- x-intercepts: (-9,0) and (-3,0)
- Minimum point: (-6,-3)
Next, pick a few additional x-values and calculate their corresponding y-values using the equation of the function.
For example:
- When x = -12, y = |-12| + 3 = 12 + 3 = 15
- When x = -8, y = |-8| + 3 = 8 + 3 = 11
- When x = 1, y = |1| + 3 = 1 + 3 = 4
Plot these additional points and connect them all with a straight line to form the graph of the absolute value function.
The final sketch of the graph will have a 'V' shape, with the minimum point at (-6,-3), and the y-intercept at (0,3). It will pass through the x-intercepts (-9,0) and (-3,0) as well.