Algebra II 3rd 9-Weeks Test

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Questions and Answers

What is a sign graph?

A sign graph (or sign chart) is a graph that displays the sign (+ or −) of a function over its domain. It is useful for visualizing where the function is positive, negative, or zero.

What is a quadratic application problem?

A quadratic application problem involves using quadratic equations to model real-world situations, such as projectile motion or optimizing areas.

Explain polynomial division.

Polynomial division is an algorithm for dividing a polynomial by another polynomial of the same or lower degree. It is analogous to long division with integers.

What is polynomial graphing?

Polynomial graphing involves plotting the graph of a polynomial function, showing its roots, intercepts, and end behavior. Signup and view all the answers

What does 'polynomial multiple-multiple' refer to?

It likely refers to problems involving finding common multiples of polynomials or factoring polynomials with multiple terms. Signup and view all the answers

What are exponent properties?

Exponent properties are rules that dictate how exponents behave when performing mathematical operations. These include the product of powers, quotient of powers, power of a power, power of a product, power of a quotient, and negative exponent properties. Signup and view all the answers

What does it mean to simplify an exponent problem?

Simplifying an exponent problem means rewriting an expression with exponents in a more concise form, often involving fewer terms or simpler exponents. Signup and view all the answers

How do you rewrite an exponential function?

Rewriting an exponential function involves changing its form without changing its value. This can include changing the base, applying exponent properties, or expressing it in logarithmic form. Signup and view all the answers

What is the graph of an exponential function?

The graph of an exponential function is a curve that either increases or decreases rapidly, depending on whether the base is greater than 1 or between 0 and 1, respectively. It has a horizontal asymptote. Signup and view all the answers

How might you analyze exponential function graphs?

Analyzing exponential function graphs involves identifying key features such as the y-intercept, asymptote, domain, range, and whether the function represents exponential growth or decay. Signup and view all the answers

What is compound interest?

Compound interest is interest calculated on the initial principal and also on the accumulated interest from previous periods. Thus, compound interest is interest on interest. Signup and view all the answers

What is a log property?

Log properties are rules that govern how logarithms behave when performing mathematical operations. These include the product rule, quotient rule, power rule, and change of base rule. Signup and view all the answers

How does an exponential function convert to logarithmic form?

An exponential equation $y = a^x$ can be converted to logarithmic form as $log_a(y) = x$, where 'a' is the base, 'x' is the exponent, and 'y' is the result. Signup and view all the answers

What does 'log multiple-multiple' refer to?

Likely refers to problems involving multiple logarithmic terms that need to be combined or simplified using logarithmic properties. Signup and view all the answers

How does an exponential/log graph relate to it's inverse?

The graph of an exponential function and its inverse logarithmic function are reflections of each other across the line $y = x$. Signup and view all the answers

What is a Polynomial Division k-problem?

This likely refers to polynomial division problems where 'k' represents an unknown constant or coefficient that needs to be determined. Signup and view all the answers

How do you find the remainder of polynomial division?

The remainder of polynomial division can be found by performing long division or synthetic division of the polynomial by the divisor. Alternatively, the Remainder Theorem can be used by evaluating the polynomial at the root of the divisor. Signup and view all the answers

How would you find a leading coefficient given information?

The leading coefficient is found by identifying the coefficient of the term with the highest degree in the polynomial. The information given is used to find the value of this coefficient through relations in the polynomial. Signup and view all the answers

How do you simplify a Log?

Logs can be simplified using the properties of logarithms, such as the product rule, quotient rule, and power rule, to combine or separate logarithmic terms. Additionally, converting to exponential form or using the change of base formula can aid simplification. Signup and view all the answers

Explain the log of log question

This refers to problems that involve nested logarithms, requiring multiple applications of logarithmic properties to simplify or solve. For example, finding the value of $log(log(x))$. Signup and view all the answers

Flashcards

Sign Graph

Illustrates positivity or negativity of function values across its domain.

Quadratic Application Problem

Applies quadratic equations to real-world scenarios to find optimal results.