Midterm Exam

Front

What is the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce based on its domain (input values).

Front

How do you reflect a graph across the y-axis?

Back

To reflect a graph across the y-axis, replace every x in the function with -x. For example, the reflection of y = |x - 1| + 7 is y = |x + 1| + 7.

Front

What is the solution to the equation x² + x = 12?

Back

The solutions are x = 3 and x = -4.

Front

What is a parent function?

Back

A parent function is the simplest form of a function type, from which other functions can be derived by transformations such as translations, reflections, and stretches.

Front

What does it mean to translate a function?

Back

Translating a function means shifting its graph horizontally and/or vertically without changing its shape.

Front

What is the effect of adding a constant to a function?

Back

Adding a constant to a function shifts the graph vertically. For example, f(x) = |x| + 2 shifts the graph of f(x) = |x| up by 2 units.

Front

What does the notation |x| represent?

Back

The notation |x| represents the absolute value of x, which is the distance of x from 0 on the number line, always resulting in a non-negative value.

Front

How do you find the vertex of a quadratic function in standard form?

Back

For a quadratic function in the form y = ax² + bx + c, the vertex can be found using the formula x = -b/(2a).

Front

What is the difference between open and closed intervals?

Back

A closed interval includes its endpoints (e.g., [a, b]), while an open interval does not include its endpoints (e.g., (a, b)).

Front

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

Back

The y-intercept is the point where the graph of the function crosses the y-axis, representing the output value when the input value (x) is zero.