Question
Question
Which function is a one-to-one function?(1 point)
Responses
r(x)=(x+8)2−2
r times x is equal to open paren x plus 8 close paren squared minus 2
c(x)=−6x−1
c times x is equal to negative 6 x minus 1
m(x)=|4x+20|+6
m times x is equal to start absolute value 4 x plus 20 end absolute value plus 6
t(x)=−2−x4
Which function is a one-to-one function?(1 point)
Responses
r(x)=(x+8)2−2
r times x is equal to open paren x plus 8 close paren squared minus 2
c(x)=−6x−1
c times x is equal to negative 6 x minus 1
m(x)=|4x+20|+6
m times x is equal to start absolute value 4 x plus 20 end absolute value plus 6
t(x)=−2−x4
Answers
GPT-4o mini
To determine which function is a one-to-one function, we need to analyze each of the given functions for whether they pass the horizontal line test, meaning that each output is associated with exactly one input.
1. **r(x) = (x + 8)² - 2**
- This is a quadratic function. Quadratic functions are not one-to-one because they can take on the same value for different inputs (for example, r(1) and r(-9) both give the same output).
2. **c(x) = -6x - 1**
- This is a linear function with a non-zero slope (-6). Linear functions with a slope that is not zero are one-to-one. This function passes the horizontal line test.
3. **m(x) = |4x + 20| + 6**
- This is an absolute value function, which is not one-to-one because it can give the same output for different inputs (for example, m(x) for positive and negative values of the expression inside the absolute value can yield the same result).
4. **t(x) = -2 - x⁴**
- This is a polynomial function with an even degree (4), which is symmetric about the y-axis and therefore not one-to-one. It can produce the same output for ±x values.
In conclusion, the only one-to-one function among the given options is:
**c(x) = -6x - 1**
1. **r(x) = (x + 8)² - 2**
- This is a quadratic function. Quadratic functions are not one-to-one because they can take on the same value for different inputs (for example, r(1) and r(-9) both give the same output).
2. **c(x) = -6x - 1**
- This is a linear function with a non-zero slope (-6). Linear functions with a slope that is not zero are one-to-one. This function passes the horizontal line test.
3. **m(x) = |4x + 20| + 6**
- This is an absolute value function, which is not one-to-one because it can give the same output for different inputs (for example, m(x) for positive and negative values of the expression inside the absolute value can yield the same result).
4. **t(x) = -2 - x⁴**
- This is a polynomial function with an even degree (4), which is symmetric about the y-axis and therefore not one-to-one. It can produce the same output for ±x values.
In conclusion, the only one-to-one function among the given options is:
**c(x) = -6x - 1**