A function, named g, has an input of c, and a range of all real numbers.
Which of the following best represents the described function?
c(g)=45g+25
c(g)=4g2−2g+1
g(c)=45c+25
g(c)=4c2−2c+1
you know that parabolas have a vertex (max or min) so their range cannot be all real numbers.
Only polynomials of odd degree will work here.
So, yes (C), since g is a function of c
The function, named g, has an input of c, and a range of all real numbers.
The expression that best represents the described function is g(c) = 4c^2 - 2c + 1.
To determine which of the given options represents the described function, we need to understand the difference between an input (usually denoted as x or c) and the mathematical function itself (usually denoted as f(x) or g(x)).
In this case, the function named "g" has an input of "c" and a range of all real numbers. The function takes the input value "c" and performs some mathematical operations on it to produce the output.
Let's analyze each of the given options:
c(g) = 45g + 25: This option represents a function that takes the input value "g," performs mathematical operations on it (multiplying by 45 and adding 25), and produces the output value "c." However, our initial information states that the function has an input of "c" and not "g", so this option does not match the described function.
c(g) = 4g^2 − 2g + 1: Similar to the previous option, this option takes the input value "g," performs mathematical operations on it (squaring, multiplying by 4, subtracting 2, and adding 1), and produces the output value "c." Again, this option does not match the described function.
g(c) = 45c + 25: This option correctly represents the described function. It indicates that the function "g" takes the input value "c," performs mathematical operations on it (multiplying by 45 and adding 25), and produces the output value "g." This matches our initial information, so this option is a valid representation of the described function.
g(c) = 4c^2 − 2c + 1: This option, like the previous one, correctly represents the described function. It indicates that the function "g" takes the input value "c," performs mathematical operations on it (squaring, multiplying by 4, subtracting 2, and adding 1), and produces the output value "g." This option is also a valid representation of the described function.
In summary, the options that best represent the described function are:
g(c) = 45c + 25
g(c) = 4c^2 − 2c + 1