Mary creates a table of values for a function and plots the points. She finds that the difference in the y values is the same. What kind of function did she graph?
How can you tell if a graph is linear, quadratic, exponential or square root?
If the difference in x values is constant and the difference in y values is constant then the slope is constant and we have a straight line.
quadratic is a parabola with one vertex
exponential curves one way
like y = e^x curves up
sqrt slope becomes smaller and smaller
Mary graphed a linear function.
To determine the type of a graph, you can consider the following characteristics:
1. Linear Function: The difference in the y-values (vertical changes) is constant. The graph of a linear function is a straight line.
2. Quadratic Function: The difference in the y-values is not constant, but the difference in the x-values (horizontal changes) is constant. The graph of a quadratic function is a parabola.
3. Exponential Function: The ratio of the y-values (vertical changes) is constant. The graph of an exponential function can have a curve that increases or decreases dramatically.
4. Square Root Function: The graph is a curve that increases but slows down as x values get larger. The graph of a square root function has a half-parabolic shape.
By analyzing the pattern of changes in the y-values, x-values, or their ratios, you can determine which type of function is represented by the graph.
To determine the type of function Mary graphed, we can look at the pattern in the differences of the y-values. Here's how you can tell if a graph is linear, quadratic, exponential, or square root:
1. Linear Function: If the differences of the y-values are consistent, meaning they have the same value, then the function is linear. Linear functions have a constant rate of change and graph as a straight line.
2. Quadratic Function: If the differences of the y-values are not consistent but instead form a pattern where the differences themselves have the same value, then the function is quadratic. Quadratic functions graph as a parabola.
3. Exponential Function: If the differences of the y-values continuously increase or decrease, then the function is exponential. Exponential functions have constant ratios between consecutive terms.
4. Square Root Function: If the differences of the y-values form a pattern where the differences decrease or increase in a consistent manner, then the function is likely a square root function. Square root functions graph as a curve that starts at the origin and grows slowly initially.
By observing the pattern in the differences of the y-values, Mary can determine the type of function she graphed.