Flashcard - Friday, November 15th

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) represent?

Back

f(x) represents the output of the function f for the input x.

Front

What is the absolute value function?

Back

The absolute value function, denoted as |x|, returns the non-negative value of x.

Front

How do you solve an absolute value equation like |x - a| = b?

Back

To solve |x - a| = b, you set up two equations: x - a = b and x - a = -b.

Front

What is the graphical representation of the function f(x) = |x + 4| + 3?

Back

The graph is a V-shape that opens upwards, with the vertex at the point (-4, 3).

Front

What does it mean for a system of equations to have no solution?

Back

A system of equations has no solution when the lines represented by the equations are parallel and never intersect.

Front

How do you solve the inequality -7 + 10z > -27?

Back

To solve the inequality, isolate z: 10z > -20, so z > -2.

Front

What is the difference between a solid line and a dashed line in graphing inequalities?

Back

A solid line indicates that the points on the line are included in the solution (≤ or ≥), while a dashed line indicates they are not included (< or >).

Front

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

Back

The vertex is the highest or lowest point of the parabola, depending on its orientation.

Front

How do you determine the number of solutions for a quadratic equation?

Back

The number of solutions can be determined using the discriminant (b² - 4ac): if it's positive, there are two solutions; if zero, one solution; if negative, no real solutions.