Question
Use the graph of the function shown.
The coordinate grid has x and y axes from negative 5 to 5. A logarithmic function is shown. A dashed asymptote is shown at x equals 1.
What are the domain and range of the logarithmic function?
(1 point)
Responses
Domain: (1,∞)
; Range: [4,∞)
Domain: open paren 1 comma infinity close paren ; Range: left bracket 4 comma infinity right parenthesis
Domain: (1,∞)
; Range: (−∞,∞)
Domain: open paren 1 comma infinity close paren ; Range: open paren negative infinity comma infinity close paren
Domain: (−∞,∞)
; Range: (1,∞)
Domain: open paren negative infinity comma infinity close paren ; Range: open paren 1 comma infinity close paren
Domain: [4,∞)
; Range: (−∞,∞)
Domain: left bracket 4 comma infinity right parenthesis ; Range: open paren negative infinity comma infinity close paren
The coordinate grid has x and y axes from negative 5 to 5. A logarithmic function is shown. A dashed asymptote is shown at x equals 1.
What are the domain and range of the logarithmic function?
(1 point)
Responses
Domain: (1,∞)
; Range: [4,∞)
Domain: open paren 1 comma infinity close paren ; Range: left bracket 4 comma infinity right parenthesis
Domain: (1,∞)
; Range: (−∞,∞)
Domain: open paren 1 comma infinity close paren ; Range: open paren negative infinity comma infinity close paren
Domain: (−∞,∞)
; Range: (1,∞)
Domain: open paren negative infinity comma infinity close paren ; Range: open paren 1 comma infinity close paren
Domain: [4,∞)
; Range: (−∞,∞)
Domain: left bracket 4 comma infinity right parenthesis ; Range: open paren negative infinity comma infinity close paren
Answers
Answered by
GPT-4o mini
For a logarithmic function with a vertical asymptote at \(x = 1\), the domain consists of all \(x\) values greater than 1, because the logarithm is undefined for \(x \leq 1\). Therefore, the domain is \((1, \infty)\).
If the range of the logarithmic function appears to extend infinitely upward from a certain point, and if you mention that the function's value reaches at least 4 and continues to extend upwards, then the range would be \([4, \infty)\).
Thus, the correct answer would be:
**Domain: (1, ∞); Range: [4, ∞)**
**Response: Domain: open paren 1 comma infinity close paren ; Range: left bracket 4 comma infinity right parenthesis**
If the range of the logarithmic function appears to extend infinitely upward from a certain point, and if you mention that the function's value reaches at least 4 and continues to extend upwards, then the range would be \([4, \infty)\).
Thus, the correct answer would be:
**Domain: (1, ∞); Range: [4, ∞)**
**Response: Domain: open paren 1 comma infinity close paren ; Range: left bracket 4 comma infinity right parenthesis**