Algebra 1, 1st Semester Final

Front

What is the range of a quadratic function?

Back

The range of a quadratic function is the set of all possible output values (y-values) based on the vertex and direction of the parabola. For example, if the vertex is at (h, k) and the parabola opens downwards, the range is given by (negative infinity, k].

Front

What is the definition of the range in 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.

Front

How do you determine the domain of a function from its graph?

Back

The domain of a function is determined by identifying all the x-values for which the function is defined. This can be seen as the horizontal extent of the graph.

Front

What is an absolute value function?

Back

An absolute value function is a function of the form f(x) = |x|, which outputs the distance of x from 0 on the number line, always resulting in a non-negative value.

Front

What transformations can be applied to an absolute value function?

Back

Transformations include vertical stretches/compressions, horizontal shifts, and vertical shifts. For example, f(x) = a|x - h| + k represents a vertical stretch by a, a horizontal shift by h, and a vertical shift by k.

Front

What is the axis of symmetry in a quadratic function?

Back

The axis of symmetry is a vertical line that divides the parabola into two mirror-image halves. It can be found using the formula x = -b/(2a) for a quadratic in the form ax^2 + bx + c.

Front

How do you write the equation of a quadratic function given its vertex?

Back

If the vertex is (h, k), the equation can be written in vertex form as f(x) = a(x - h)^2 + k, where 'a' determines the direction and width of the parabola.

Front

What is the vertex of a quadratic function?

Back

The vertex is the highest or lowest point of the parabola, depending on whether it opens upwards or downwards. It can be found using the formula (h, k) where h = -b/(2a) and k is the function value at h.

Front

What does it mean for a function to be increasing or decreasing?

Back

A function is increasing on an interval if the output values rise as the input values increase. It is decreasing if the output values fall as the input values increase.

Front

What is the difference between a function's domain and range?

Back

The domain is the set of all possible input values (x-values) for the function, while the range is the set of all possible output values (y-values) produced by the function.