Which function is not a one-to-one function?(1 point)

Question

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

Answer 1

To determine which function is not a one-to-one function, we need to analyze each of the provided functions:

1. \( n(x) = -2(2.4)^x \): This is an exponential function, which is one-to-one.

2. \( z(x) = 6 - \sqrt{3 - x} \): This function is defined as long as \( 3 - x \geq 0 \) (or \( x \leq 3 \)). The square root function can yield the same output for different inputs (for example, \( \sqrt{2} \) generates the same output for both inputs \( 2 \) and \( 2 \)). Therefore, it needs further investigation, but a square root does tend to restrict the range of inputs.

3. \( c(x) = -x^2 + 8x - 20 \): This is a quadratic function that opens downward (due to the negative coefficient of \( x^2 \)). Quadratic functions are not one-to-one unless they are restricted to a domain that includes only one side of the vertex. In its full domain, this function fails the horizontal line test and is not one-to-one.

4. \( v(x) = -2 \ln(x + 1) + 3 \): This is a logarithmic function, which is one-to-one because it increases monotonically over its domain.

Based on the analysis, \( c(x) = -x^2 + 8x - 20 \) is not a one-to-one function because it is a quadratic function that does not pass the horizontal line test.