Function Features Flashcards
What is an axis of symmetry?
a vertical line cutting a parabola in two symmetrical halves (written in the form x=___)
What is a horizontal asymptote?
a horizontal line that a function approaches but never touches (written in the form y=___)
What is a vertical asymptote?
a vertical line that a function approaches but never touches (written in the form x=___)
What is a local minimum?
a relative low-point (where a function transitions from decreasing to increasing)
What is a local maximum?
a relative high-point (where a function transitions from increasing to decreasing)
x is the ______
f(x) is the _____
x is the input
f(x) is the output
How do you find the axis of symmetry of a quadratic function?
2 ways:
1) use the graphing calculator to find the x-value of the minimum or maximum, then the axis of symmetry is x = ____.
2) Use the formula from the formula book:
x = -b/2a
How do you find the horizontal asymptote?
1) graph the function
2) press trace
3) move the cursor to the right or left until the y-value settles to a value
How do you find the vertical asymptote?
1) graph the function
2) press trace
3) move the cursor to the right or left until the y-value output is blank (or there is an error). In this example, when x=0, there is no output, that means the vertical asymptote is x=0.
How do you find the maximum or minimum?
1) Enter equation into the y-editor (Y=)
2) Press graph. You may need to adjust the window so that the max or min is in view.
3) Press 2nd, trace, 3: minimum or 4: maximum
4) Using the left and right arrows, move your cursor to the left side of the max or min. Press enter. Move your cursor to the right side of the max or min. Press enter. Then press enter one last time.
The calculator should now tell you the x and y values of the maximum or minimum point.
How do you find the intersection of two lines?
1) Enter equations into the y-editor (Y=)
Y1= first equation
Y2= second equation
2) Press graph. You may need to adjust your window so that you can see the intersection point.
3) Press 2nd, trace, 5: intersect
4) Use the left and right arrows to move your cursor near the intersection. Press enter. The cursor should jump to the other line. Press enter again. Then press enter one last time.
The calculator should now tell you the x-value and y-value of the intersection point.
What are two other words for x-intercept?
Zeroes, roots
How do you find the zeroes of a function?
1) Enter equation into the y-editor (Y=)
2) Press graph
3) Press 2nd, trace, 2: zero
4) Using the left and right arrows, move your cursor to the left side of the zero. Press enter. Move your cursor to the right side of the zero. Press enter. Then press enter one last time.
The calculator should now tell you the x-value when y is zero.
What is an x-intercept?
where a line crosses the x-axis (x, 0)
What is a y-intercept?
where a line crosses the y-axis (0, y)
How could you find when a line y=3x^2 reaches a y-value of 100, using the graphing feature on your calculator?
Graph y= 3x^2 and y=100. Then see where these lines intersect.
