Midterm exam review 2024

Front

What is the definition of a solution in the context of a graph?

Back

A solution refers to the point(s) where the graph intersects the x-axis, indicating the values of x for which the function equals zero.

Front

How do you determine the number of solutions a graph has?

Back

By analyzing the points where the graph intersects the x-axis. If it does not intersect, it has no solutions; if it intersects at one point, it has one solution; if it intersects at two points, it has two solutions.

Front

Back

Front

What is the definition of a function?

Back

A function is a relation that assigns exactly one output for each input from its domain.

Front

What does the notation f(x) = |x + 2| - 4 represent?

Back

This represents an absolute value function that shifts the basic absolute value graph left by 2 units and down by 4 units.

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.

Front

How do you find the range of the function f(x) = |x + 2| - 4?

Back

The minimum value occurs at x = -2, where f(-2) = 0 - 4 = -4. Therefore, the range is all values greater than or equal to -4: y ≥ -4.

Front

What transformations are represented by g(x) = f(x + 4) - 6?

Back

This represents a horizontal shift 4 units to the left and a vertical shift 6 units down.

Front

What is the vertex of the function f(x) = |x + 2| - 4?

Back

The vertex is the point (-2, -4), which is the minimum point of the graph.

Front

What does it mean for a function to have no solutions?

Back

It means that the graph of the function does not intersect the x-axis, indicating there are no values of x for which the function equals zero.