Answer: See explanation
Explanation:
For questions 1 - 4, it's asking you to plug in numbers into the original functions.
1. f(-2): You would plug -2 into f(x) = 2x^2 - 3x, getting
2(-2)^2 - 3(-2)
2(4) - (-6)
8 + 6 = 14
f(-2) = 14
2. f(x) - g(x): You're basically just subtracting the two functions
(2x^2 - 3x) - (2 - 5x)
2x^2 - 3x - 2 + 5x
Combine like terms
2x^2 + 2x - 2
3. You're multiplying them so (2x^2 - 3x)(2 - 5x)
4. f(g(x)): It's like f(-2), but instead of -2, you plug in the function of g(x)
So in 2x^2 - 3x, x would equal 2 - 5x:
2(2 - 5x)^2 - 3(2 - 5x)
And then simplify that.
For questions 5 - 6, it's asking for shifting from the parent function. Parent function is always f(x) or g(x) or whatever variable it is.
5. f(x - 8) + 9: The 9 is the y value shift, meaning the parent function is shifted up 9 units. For -8, think of what x needs to be for (x - 8) to be 0. If that number is positive, function shifts right; if negative, shift left. In this case, x needs to be 8 in order for (x - 8) to be 0. Therefore, f(x) is shifted right 8 units.
6. -3f(x) - 2: From the previous question, we now know that -2 means f(x) is shifted down 2 units. When you have 3f(x), you're multiplying the entire function by 3, so it's called a vertical stretch of 3. The negative means it's reflected over the x-axis since the y value is the opposite of what it used to be.