Semester Exam PreCalculus Study Guide B

Front

What is the transformed equation for the graph of y = log(x)?

Back

y = log(x + 4) is a transformation that shifts the graph 4 units to the left.

Front

How many radians are in a full rotation of a circle?

Back

A full rotation of a circle is measured in 2π radians.

Front

What is the value of cos(90°) based on the unit circle?

Back

cos(90°) = 0.

Front

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

Back

Yes, (x-2) is a factor. The remainder is zero.

Front

What are the zeros of the polynomial h(x) = x⁴ + 3x³ - 55x² - 99x + 630?

Back

The zeros are -5, 6, 3, -7.

Front

What is the definition of a logarithm?

Back

A logarithm is the inverse operation to exponentiation, answering the question: to what exponent must a base be raised to produce a given number?

Front

What is the relationship between degrees and radians?

Back

180 degrees is equal to π radians.

Front

What is the formula for the area of a circle?

Back

The area A of a circle is given by A = πr², where r is the radius.

Front

What is the quadratic formula?

Back

The quadratic formula is x = (-b ± √(b² - 4ac)) / (2a) for the equation ax² + bx + c = 0.

Front

What is the definition of a polynomial function?

Back

A polynomial function is a function that can be expressed in the form f(x) = a_nx^n + a_(n-1)x^(n-1) + ... + a_1x + a_0, where a_n, a_(n-1), ..., a_0 are constants and n is a non-negative integer.