Algebra 1 Shapes of Graphs Flashcard

Front

What are extrema in a graph?

Back

Extrema are the maximum and minimum values of a function on a given interval. They indicate the highest and lowest points on the graph.

Front

How do you determine the number of extrema in a graph?

Back

To determine the number of extrema, analyze the critical points where the derivative is zero or undefined, and evaluate the function at these points.

Front

What is a line of symmetry in a graph?

Back

A line of symmetry is a line that divides a graph into two mirror-image halves. If a graph has no symmetry, it means it does not reflect across any line.

Front

What does it mean for a function to be increasing?

Back

A function is increasing on an interval if, as the input values increase, the output values also increase.

Front

What is a maximum point on a graph?

Back

A maximum point is a point on the graph where the function value is greater than the function values at nearby points.

Front

What is a minimum point on a graph?

Back

A minimum point is a point on the graph where the function value is less than the function values at nearby points.

Front

How can you identify the intervals where a function is increasing or decreasing?

Back

To identify intervals of increase or decrease, analyze the sign of the derivative of the function. If the derivative is positive, the function is increasing; if negative, it is decreasing.

Front

What is the significance of the y-coordinate in determining the minimum value of a function?

Back

The y-coordinate at the minimum point indicates the lowest value that the function can attain.

Front

What does it mean if a graph has no symmetry?

Back

If a graph has no symmetry, it means that it does not exhibit reflective properties across any axis or line.

Front

How do you find the coordinates of extrema?

Back

To find the coordinates of extrema, calculate the derivative of the function, set it to zero to find critical points, and evaluate the function at these points.