Final Exam Review

Front

What does the inequality 2x - 3 < -7 represent on a graph?

Back

The graph represents all the values of x that make the inequality true, which is the region to the left of the point where the line 2x - 3 = -7 intersects the x-axis.

Front

How do you solve the equation -2x + 18 = 2x + 40?

Back

Combine like terms: 18 - 40 = 2x + 2x; -22 = 4x; x = -5.5.

Front

What happens to the graph of a quadratic function when the value of 'a' is negative?

Back

The graph is reflected downwards, opening towards the negative y-axis.

Front

What is the vertical line test?

Back

A method to determine if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

Which graph does NOT pass the vertical line test?

Back

Graph 1 does not pass the vertical line test.

Front

What does it mean if an equation has infinitely many solutions?

Back

It means that there are countless values of x that satisfy the equation, often resulting from equivalent expressions.

Front

What is the solution to the equation 3(x − 2) = 3x − 6?

Back

The equation simplifies to 0 = 0, indicating infinitely many solutions.

Front

What is a quadratic function?

Back

A polynomial function of degree 2, typically in the form f(x) = ax^2 + bx + c.

Front

What does it mean for a function to be linear?

Back

A function is linear if it can be graphically represented as a straight line, typically in the form f(x) = mx + b.

Front

What is the significance of the 'a' value in a quadratic function?

Back

The 'a' value determines the direction of the parabola; if 'a' is positive, it opens upwards, and if negative, it opens downwards.