Algebra 2
Exponential, Logarithmic, and Inverse Functions flashcards
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- In Exponential Growth and Decay, what does initial value and base mean?Exponential Growth and Decay
- The starting quantity and repeated growth factor.
- What is y at t=0?Exponential Growth and Decay
- A because b⁰=1.
- In Exponential Growth and Decay, what does decay factor mean?Exponential Growth and Decay
- A multiplier below one describing exponential decay.
- Does a 20% loss subtract the same amount each period?Exponential Growth and Decay
- No, it subtracts a share of the changing amount.
- In Exponential Growth and Decay, what does percent change and context mean?Exponential Growth and Decay
- A percent change converted to a multiplicative factor.
- Why identify the period length?Exponential Growth and Decay
- Monthly and yearly rates are not interchangeable without conversion.
- In Inverse Functions, what does one-to-one requirement mean?Inverse Functions
- A rule with no repeated outputs on its stated domain.
- What graphical test checks this?Inverse Functions
- Every horizontal line meets the graph at most once.
- In Inverse Functions, what does swapping inputs and outputs mean?Inverse Functions
- An algebraic procedure for an inverse function.
- Why exchange domain and range?Inverse Functions
- Original outputs become inverse inputs.
- In Inverse Functions, what does inverse graphs mean?Inverse Functions
- A mirror relationship between a function and its inverse.
- Must the full quadratic have an inverse function over all reals?Inverse Functions
- No, it repeats outputs unless its domain is restricted.
- In Logarithms as Inverses, what does logarithm definition mean?Logarithms as Inverses
- The inverse operation of exponentiation.
- Can log_b(0) be real?Logarithms as Inverses
- No, real logarithm arguments must be positive.
- In Logarithms as Inverses, what does equivalent forms mean?Logarithms as Inverses
- Two notations for one base-power relationship.
- What base values are allowed?Logarithms as Inverses
- Positive bases other than one.
- In Logarithms as Inverses, what does logarithm graph mean?Logarithms as Inverses
- A graph obtained by reflecting an exponential across y=x.
- Why is x=0 excluded?Logarithms as Inverses
- The logarithm input must be positive.
- In Logarithm Properties and Equations, what does product rule mean?Logarithm Properties and Equations
- The logarithm identity for positive factors.
- Can log_b(M+N) split the same way?Logarithm Properties and Equations
- No, there is no general log-sum rule.
- In Logarithm Properties and Equations, what does quotient and power rules mean?Logarithm Properties and Equations
- Two logarithm transformations with domain conditions.
- Why require positive arguments?Logarithm Properties and Equations
- Real logarithms are undefined for zero or negative inputs.
- In Logarithm Properties and Equations, what does solving and checking mean?Logarithm Properties and Equations
- Domain-aware checking of a logarithmic equation.
- Can algebra produce an invalid candidate?Logarithm Properties and Equations
- Yes, manipulating logarithms can conceal a forbidden argument.
- In Exponential and Logarithmic Models, what does compound growth mean?Exponential and Logarithmic Models
- An exponential model for recurring proportional change.
- What does a model base encode?Exponential and Logarithmic Models
- The factor applied during each time interval.
- In Exponential and Logarithmic Models, what does half-life mean?Exponential and Logarithmic Models
- An exponential decay measure by equal half periods.
- What remains after two half-lives?Exponential and Logarithmic Models
- One quarter of the initial amount.
- In Exponential and Logarithmic Models, what does logarithmic time mean?Exponential and Logarithmic Models
- Finding an exponent from a target amount.
- Why check target and initial value signs?Exponential and Logarithmic Models
- The real logarithm argument must be positive.