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

Answer 1

A function is considered one-to-one if it passes the horizontal line test, meaning that no horizontal line intersects the graph of the function more than once. Let's analyze each of the given functions:

1. **r(x) = (x + 8)² - 2**: This is a quadratic function, which is not one-to-one because it is a parabola that opens upwards. A horizontal line can intersect it at two points.

2. **c(x) = -6x - 1**: This is a linear function with a non-zero slope. Linear functions are one-to-one because any horizontal line will intersect it at most once.

3. **m(x) = |4x + 20| + 6**: The absolute value function is not one-to-one because it can take the same value for different inputs (e.g., both x = -10 and x = 10 yield the same result for this function).

4. **t(x) = -2 - x⁴**: This function is not one-to-one as well because it is a quartic function that opens downwards and can also potentially repeat values for different x.

Thus, the only one-to-one function among the options provided is:

**c(x) = -6x - 1**.