Given the parent functions f(x) = 5x + 1 and g(x) = 3x + 9, what is g(x) – f(x)?

To find g(x) – f(x), we first need to write out both parent functions:

• f(x) = 5x + 1
• g(x) = 3x + 9

Now, we will substitute these expressions into the equation:

g(x) - f(x) = (3x + 9) - (5x + 1)

Next, we simplify this by distributing the negative sign and combining like terms:

g(x) - f(x) = 3x + 9 - 5x - 1

g(x) - f(x) = (3x - 5x) + (9 - 1)

Combining these results gives:

g(x) - f(x) = -2x + 8

So, the final answer is:

g(x) - f(x) = -2x + 8

This tells us how the two functions relate to each other across their domains.