MTH 161 Final Exam Review

Front

What is the average rate of change of a function over an interval?

Back

The average rate of change of a function f(x) over the interval [a, b] is given by the formula: \( \frac{f(b) - f(a)}{b - a} \). It represents the slope of the secant line connecting the points (a, f(a)) and (b, f(b)).

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

What is end behavior in the context of functions?

Back

End behavior describes the behavior of a function as the input values approach positive or negative infinity. It helps in understanding the long-term trends of the function's graph.

Front

What does the limit \( \lim_{x\rightarrow c} f(x) \) represent?

Back

The limit \( \lim_{x\rightarrow c} f(x) \) represents the value that f(x) approaches as x gets arbitrarily close to c. It is a fundamental concept in calculus used to define continuity and derivatives.

Front

What is Gaussian Elimination?

Back

Gaussian Elimination is a method for solving systems of linear equations. It involves using row operations to transform the system's augmented matrix into row-echelon form, making it easier to find solutions.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does HA stand for in the context of functions?

Back

HA stands for Horizontal Asymptote. It is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Tags

CCSS.HSF-IF.C.7D

Front

How do you find the average rate of change of a function on the interval [1, 5]?

Back

To find the average rate of change on the interval [1, 5], calculate \( \frac{f(5) - f(1)}{5 - 1} \). Substitute the values of the function at x=1 and x=5.

Tags

CCSS.HSF.IF.B.6

CCSS.8.F.B.4

Front

What is the significance of a limit being undefined?

Back

A limit being undefined indicates that the function does not approach a specific value as x approaches a certain point, often due to discontinuities or vertical asymptotes.

Front

What is the difference between a horizontal asymptote and a vertical asymptote?

Back

A horizontal asymptote describes the behavior of a function as x approaches infinity, while a vertical asymptote describes the behavior of a function as x approaches a specific value where the function is undefined.

Tags

CCSS.HSF-IF.C.7D

Front

What is the solution to the system of equations using Gaussian Elimination?

Back

The solution to a system of equations using Gaussian Elimination is the set of values for the variables that satisfy all equations in the system, often represented as an ordered pair or triplet.

Tags

CCSS.HSA.REI.C.6

CCSS.8.EE.C.8B

Front

What does it mean if a function has no horizontal or vertical asymptotes?

Back

If a function has no horizontal or vertical asymptotes, it means that the function does not approach a constant value as x approaches infinity or does not become undefined at any finite value of x.

Tags

CCSS.HSF-IF.C.7D