IM2 Fall 2024 Semester Exam (HONORS)

Front

What is the effect of a vertical stretch by a factor of 3 on the function f(x)?

Back

The graph of the function is stretched vertically, making it steeper. For example, if f(x) = x^2, then after stretching, it becomes f(x) = 3x^2.

Front

How does reflecting a function down affect its graph?

Back

Reflecting a function down means that all y-values are multiplied by -1. For example, if f(x) = x^2, after reflection it becomes f(x) = -x^2.

Front

What does it mean to shift a function left by 1 unit?

Back

Shifting a function left by 1 unit means to replace x with (x + 1) in the function. For example, f(x) = x^2 becomes f(x) = (x + 1)^2.

Front

What is the quadratic formula?

Back

Front

What does the vertex of a parabola represent?

Back

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

Front

How do you determine if a quadratic function opens upwards or downwards?

Back

A quadratic function opens upwards if the coefficient of x^2 (a) is positive, and it opens downwards if a is negative.

Front

What is the significance of the y-intercept in a quadratic function?

Back

The y-intercept is the point where the graph intersects the y-axis, which occurs when x = 0. It can be found by evaluating f(0).

Front

What is the average rate of change of a function?

Back

The average rate of change of a function between two points is calculated as the change in the function's value divided by the change in x, or (f(b) - f(a)) / (b - a).

Front

What characterizes a linear function?

Back

A linear function is characterized by a constant rate of change and can be represented by the equation y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

A quadratic function is a polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c, where a, b, and c are constants.