Podcast
Questions and Answers
The function $f(x) = log_3(x)$ has a domain of all real numbers.
The function $f(x) = log_3(x)$ has a domain of all real numbers.
False (B)
The graph of $f(x) = log_3(x)$ has a y-intercept at (0, 1).
The graph of $f(x) = log_3(x)$ has a y-intercept at (0, 1).
False (B)
The function $f(x) = log_{\frac{1}{2}}(x) + 3$ has a vertical asymptote at $x = 3$.
The function $f(x) = log_{\frac{1}{2}}(x) + 3$ has a vertical asymptote at $x = 3$.
False (B)
As $x$ approaches infinity for the function $f(x) = log_{\frac{1}{2}}(x) + 3$, $f(x)$ approaches positive infinity.
As $x$ approaches infinity for the function $f(x) = log_{\frac{1}{2}}(x) + 3$, $f(x)$ approaches positive infinity.
The graph of $f(x) = log_4(x + 5)$ is a transformation of $log_4(x)$ shifted 5 units to the right.
The graph of $f(x) = log_4(x + 5)$ is a transformation of $log_4(x)$ shifted 5 units to the right.
The range of the function $f(x) = log_4(x+5)$ is all real numbers.
The range of the function $f(x) = log_4(x+5)$ is all real numbers.
The function $f(x) = log_3(x)$ has an x-intercept at (1, 0).
The function $f(x) = log_3(x)$ has an x-intercept at (1, 0).
The graph of $f(x) = log_4(x + 5)$ has a y-intercept at $(0, log_4(5))$.
The graph of $f(x) = log_4(x + 5)$ has a y-intercept at $(0, log_4(5))$.
The asymptote of $f(x) = log_3(x)$ is $y = 0$.
The asymptote of $f(x) = log_3(x)$ is $y = 0$.
The domain of $f(x) = log_4(x + 5)$ is $x > 5$.
The domain of $f(x) = log_4(x + 5)$ is $x > 5$.
Flashcards
Domain
Domain
The set of all possible input values (x-values) for which a function is defined.
Range
Range
The set of all possible output values (y-values) of a function.
End Behavior
End Behavior
Describes the trend of the function's output as the input approaches positive or negative infinity.
x-intercept
x-intercept
Signup and view all the flashcards
Asymptote
Asymptote
Signup and view all the flashcards
Logarithmic Function
Logarithmic Function
Signup and view all the flashcards
Logarithmic Domain Restriction
Logarithmic Domain Restriction
Signup and view all the flashcards
Vertical Shift
Vertical Shift
Signup and view all the flashcards
Horizontal Shift
Horizontal Shift
Signup and view all the flashcards
Study Notes
- The homework is on graphing logarithmic functions.
- Instructions include graphing each function and identifying its key characteristics.
Function 1: f(x) = log₃(x)
- Need to determine the domain, range, end behavior, x-intercept, and asymptote.
Function 2: f(x) = log₁/₂(x) + 3
- Need to determine the domain, range, end behavior, x-intercept, and asymptote.
Function 3: f(x) = log₄(x+5)
- Need to determine the domain, range, end behavior, x-intercept, and asymptote.
Studying That Suits You
Use AI to generate personalized quizzes and flashcards to suit your learning preferences.
