Hi! How do you do question 2 on page 100 from the functions section? I reviewed the solution in the back of the book but still don’t understand.
g(x) = 1/5 (5)^(x+4)
For the given function g, which of the following equivalent forms shows the y-coordinate of the y-intercept of the graph of y=g(x) in the xy-plane as a constant or coefficient?
A. g(x) = 125(5)^x
B. g(x) = 25(5)^(x+1)
C. g(x) = 5(5)^(x+2)
D. g(x) = (5)^(x+3)
Choice A is correct, but why?
The function f is defined by a polynomial. Some values of x and f(x) are shown in the table above. Which of the following could define f?
A) (x – 5) (x + 2)
B) (x + 5)^2 (x – 2)^3
C) x^2 (x + 5) (x – 2)^2
D) x (x + 5) (x – 2)
Specifically, can you explain why C is correct but D cannot be?
if f(2x+3)=4x-7 for all values of x, for what value of t is f(t)=1
For #2 on the functions chapter, could you have just added 1 to each side to get f(x) by itself?
I’m having trouble wrapping my head around your previous explanations and wanted to confirm that this method works.
Hi! May you please explain how to find the function for f(x) for number 5 from the practice questions in the “functions” chapter? I saw the solution, which said to find f(5+3), and then I got the correct answer, but I wanted to see if there is a function that could be found (as I tried to find it but I found it incorrectly and got an incorrect answer).
How do you do Test 9 section 3 number 20?
test 9 section 3 number 18
f(x) = √x
g(x) = 3x – b
If the graph of y = f(g(x)) passes through (6, 5) in the standard (x, y) coordinate plane, what is the value of b?
I’m having a lot of trouble with this problem, could you please break it down for me? It is number 2 on the functions practice questions. “If f(x-1)=x+1 for all values of x, which of the following is equal to f(x+1)?”
The way to think about this (for me, anyway) begins with understanding that 2[something] + 3 = 8x – 1, and our job is to figure out what that something is. Since this question gives us answer choices, all we really need to do is try each one as the something to see what works. Since (more…)
Think of it this way: the g function is doing SOME AS-YET-UNKNOWN THINGS to (–x + 7) to turn it into (2x + 1). Of the simple mathematical operations probably at play here (addition, subtraction, multiplication, division) what could be going on? First, the only way you go from –x to 2x is you multiply by –2. So (more…)
The thing to remember about functions is that they do the same thing to whatever is inside the parentheses. So don’t worry about the r vs. the h. They could use x, or a little star symbol, or whatever else they want. What matters is that the function f, as defined here, will equal zero (more…)
A function will only have that property if it’s a line that passes through the origin. For example, f(x) = 5x has that property: You can try the same with other linear functions to see why they won’t work. For example, if f(x) = 5x + 2: Nonlinear functions also won’t work. For example, if f(x) (more…)
Thank you, Mike, for your ever-awesome explanations! Here’s a question from April 2017 SAT: