X-Intercept
What is an x-intercept?
The point where the graph intersects the x-axis (where y=0).
What is a y-intercept?
The point where the graph intersects the y-axis (where x=0).
What are zeros of a function?
The values of x for which f(x)=0.
What is an increasing interval?
An interval where the function values are increasing as x increases.
What is a maximum point?
The highest point on the graph within a given interval.
How do you find the x-intercept?
Set y=0 in the function and solve for x.
How do you find the y-intercept?
Set x=0 in the function and solve for y.
How do you find the roots of a polynomial?
Use factoring, the quadratic formula, or synthetic division to find roots.
What is a decreasing interval?
An interval where the function values are decreasing as x increases.
What is a minimum point?
The lowest point on the graph within a given interval.
Give an example of a function with two x-intercepts.
Example: f(x)=x2−4 has x-intercepts at x=−2 and x=2.
Give an example of a function with a y-intercept of zero.
Example: The function f(x)=3x has a y-intercept of zero at the origin (0, 0).
Why are roots important in graphing?
Roots are important because they indicate where the graph crosses the x-axis, showing solutions to equations.
Define a positive interval.
A positive interval is where f(x)>0.
How do you find the relative maximum of a function?
Find the highest point in the given area.
How does an x-intercept relate to a quadratic function?
The x-intercepts of a quadratic function represent the roots of the equation ax2+bx+c=0.
How do y-intercepts impact the graph of a linear function?
The y-intercept indicates the starting value of a linear function when x=0.
Explain how to determine the number of roots from a graph.
Count the points where the graph touches or crosses the x-axis to determine the number of roots.
Define a negative interval.
A negative interval is where f(x)<0 .
How do you find the relative minimum of a function?
Find the lowest point in the given area.
What is the significance of the x-intercept in real-life applications?
The x-intercept can indicate where a quantity reaches zero, such as profit or loss in a business context.
Explain how the y-intercept can indicate trends in data.
The y-intercept can show trends, for example, the initial cost in a cost-revenue analysis.
What role do roots play in solving equations?
Roots are essential for finding solutions to equations and analyzing function behavior.
How can you identify maximum and minimum intervals on a graph?
They are the highest and lowest points in a given range.
Explain the importance of maximum and minimum points.
It's the highest and lowest points within the given range