Question
Question
Which function is not a one-to-one function?(1 point)
Responses
n(x)=−2(2.4)x
n times x is equal to negative 2 times 2 point 4 to the x th power
z(x)=6−3−x−−−−−√
z times x is equal to 6 minus square root of 3 minus x end root
c(x)=−x2+8x−20
c times x is equal to negative x squared plus 8 x minus 20
v(x)=−2ln(x+1)+3
Which function is not a one-to-one function?(1 point)
Responses
n(x)=−2(2.4)x
n times x is equal to negative 2 times 2 point 4 to the x th power
z(x)=6−3−x−−−−−√
z times x is equal to 6 minus square root of 3 minus x end root
c(x)=−x2+8x−20
c times x is equal to negative x squared plus 8 x minus 20
v(x)=−2ln(x+1)+3
Answers
GPT-4o mini
To determine which function is not a one-to-one function, we need to assess each option:
1. **n(x) = −2(2.4)^x**: This function is an exponential function. Exponential functions are one-to-one because they pass the horizontal line test; that is, for each x-value, there is a unique y-value.
2. **z(x) = 6 − √(3 − x)**: The square root function here is only defined for values where \(3 - x \geq 0\) (i.e., \(x \leq 3\)). This function is also one-to-one since it is decreasing; each input corresponds to a unique output.
3. **c(x) = −x^2 + 8x - 20**: This function is quadratic, and graphs of quadratic functions are parabolas. Quadratic functions are not one-to-one because they fail the horizontal line test; they have the same output for two different input values when the x-values are symmetrically positioned about the vertex.
4. **v(x) = −2ln(x + 1) + 3**: The logarithmic function here is one-to-one if defined properly (i.e., for \(x > -1\)), and the negative coefficient maintains its one-to-one property.
Based on this analysis, the function that is **not a one-to-one function** is:
**c(x) = -x² + 8x - 20** (quadratic function).
1. **n(x) = −2(2.4)^x**: This function is an exponential function. Exponential functions are one-to-one because they pass the horizontal line test; that is, for each x-value, there is a unique y-value.
2. **z(x) = 6 − √(3 − x)**: The square root function here is only defined for values where \(3 - x \geq 0\) (i.e., \(x \leq 3\)). This function is also one-to-one since it is decreasing; each input corresponds to a unique output.
3. **c(x) = −x^2 + 8x - 20**: This function is quadratic, and graphs of quadratic functions are parabolas. Quadratic functions are not one-to-one because they fail the horizontal line test; they have the same output for two different input values when the x-values are symmetrically positioned about the vertex.
4. **v(x) = −2ln(x + 1) + 3**: The logarithmic function here is one-to-one if defined properly (i.e., for \(x > -1\)), and the negative coefficient maintains its one-to-one property.
Based on this analysis, the function that is **not a one-to-one function** is:
**c(x) = -x² + 8x - 20** (quadratic function).