Big Review #3 (Passwater questions)

Front

What can be said about the inverse of a function that is increasing and concave up?

Back

The inverse function is increasing and concave down.

Front

What is the end behavior of a polynomial function of odd degree?

Back

As x approaches positive infinity, the function approaches positive infinity; as x approaches negative infinity, the function approaches negative infinity.

Front

How many distinct real zeros does the polynomial f(x) = (x+1)(x^2 - 3x - 4) have?

Back

f has exactly two distinct real zeros.

Front

What is the least possible degree of a polynomial function given a set of values?

Back

The least possible degree is determined by the number of changes in direction of the graph, which corresponds to the number of zeros.

Front

What transformations are applied to a function when it is horizontally translated by -4 units, vertically dilated by a factor of 2, and vertically translated by 3 units?

Back

The function k(x) = 2h(x+4) + 3 relates to h after these transformations.

Front

Define 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 does it mean for a function to be concave up?

Back

A function is concave up if its second derivative is positive, indicating that the graph of the function opens upwards.

Front

What does it mean for a function to be concave down?

Back

A function is concave down if its second derivative is negative, indicating that the graph of the function opens downwards.

Front

What is the significance of the degree of a polynomial function?

Back

The degree of a polynomial function determines the maximum number of real zeros and the end behavior of the function.

Front

What is the relationship between the increasing/decreasing nature of a function and its inverse?

Back

If a function is increasing, its inverse is also increasing; if a function is decreasing, its inverse is also decreasing.