Pre-Test UB SUMMER ACADEMY

Front

What is the minimum value of the function f(x) = x² - 7?

Back

-7

Front

What is the composition of functions (g∘f)(x) if f(x) = 2x + 1 and g(x) = 3x + 2?

Back

6x + 5

Front

Multiply the polynomials (x³ - x² - 5)(-x - 3). What is the result?

Back

-x⁴ - 2x³ + 3x² + 5x + 15

Front

What is the degree of the expression x⁵z² + 7?

Back

7

Front

Write the equation representing the total cost y for x people going on a cruise that costs $800 per person with a $150 booking fee.

Back

y = 800x + 150

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.

Front

What is the difference between a linear function and a quadratic function?

Back

A linear function has the form f(x) = mx + b, where m and b are constants, while a quadratic function has the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

How do you find the vertex of a quadratic function in the form f(x) = ax² + bx + c?

Back

The vertex can be found using the formula x = -b/(2a) and then substituting this x-value back into the function to find the corresponding y-value.

Front

What is the significance of the leading coefficient in a polynomial function?

Back

The leading coefficient determines the end behavior of the polynomial function; if it is positive, the function rises to the right, and if negative, it falls to the right.

Front

What is the formula for the area of a rectangle?

Back

Area = length × width.