Math 3 Midterm Review Unit 1/2

Front

What is interval notation?

Back

Interval notation is a way of representing a range of numbers using brackets and parentheses. For example, [-14.5, 0.5) represents all numbers from -14.5 to 0.5, including -14.5 but not including 0.5.

Front

Solve f(-3) = -10 | x - 9 | + 8. What is the value of f(-3)?

Back

f(-3) = -112.

Front

What does the equation |v + 8| − 5 = 2 represent?

Back

This equation represents an absolute value equation, which can have two cases: v + 8 - 5 = 2 or -(v + 8) - 5 = 2.

Front

What are the solutions to the equation |v + 8| − 5 = 2?

Back

The solutions are v = -1 and v = -15.

Front

How do you solve for real roots of a polynomial?

Back

To solve for real roots, set the polynomial equal to zero and factor or use the quadratic formula if applicable.

Front

What are the real roots of the equation x^2 - 5x + 4 = 0?

Back

The real roots are x = 4 and x = 1.

Front

What does it mean if an equation has 'No Solution'?

Back

'No Solution' means that there are no values of the variable that satisfy the equation.

Front

What is the solution to the equation x^2 + 2x + 5 = 0?

Back

The equation has No Solution because the discriminant is negative.

Front

What is the difference between closed and open intervals in interval notation?

Back

Closed intervals include their endpoints (e.g., [a, b]), while open intervals do not (e.g., (a, b)).

Front

How do you express the solution set of x < 3 in interval notation?

Back

The solution set is expressed as (-∞, 3).