Graphs of Functions

Front

What is the relationship between weight and spring stretch in Hooke's Law?

Back

The stretch of a spring is directly proportional to the weight applied to it, described by the equation y = kx, where k is the spring constant.

Front

How do you calculate the stretch of a spring per ounce of weight?

Back

Divide the total stretch of the spring by the total weight applied. For example, if 15 ounces stretches the spring 7.5 inches, then the stretch per ounce is 7.5 inches / 15 ounces = 0.5 inches per ounce.

Front

What is an exponential function?

Back

An exponential function is a mathematical function of the form y = a * b^x, where a is a constant, b is the base, and x is the exponent.

Front

Will the graph of the function y = 2^x ever cross the x-axis?

Back

No, the graph of y = 2^x will never cross the x-axis because exponential functions are always positive for all real x.

Front

What does the equation y = 60(1/2)^x represent in a real-world context?

Back

This equation represents exponential decay, where the quantity starts at 60 and decreases by half for each unit increase in x.

Front

How do you find the coordinates of a function from its equation?

Back

Substitute values of x into the function's equation to find the corresponding y values, creating coordinate pairs (x, y).

Front

What is the significance of the vertex in the graph of a quadratic function?

Back

The vertex represents the maximum or minimum point of the parabola, depending on the direction it opens.

Front

What is the standard form of a quadratic function?

Back

The standard form of a quadratic function is y = ax^2 + bx + c, where a, b, and c are constants.

Front

How do you determine if a coordinate pair is on the graph of a function?

Back

Substitute the x-value of the coordinate pair into the function's equation and see if the resulting y-value matches the y-value of the pair.

Front

What is the difference between linear and quadratic functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while quadratic functions have a variable rate of change and graph as parabolas.