f(x)=8x^2-6; horizontal stretch by a factor of 2 and a translation 2 units up, followed by a reflection in the y-axis

Question

Please help asap

Answer 1

The general rules of transformations are a f(b(x-h)) + k

k - vertical shift up/down

h - horizontal shift down/up (the opposite) - That's why it says -h. So h=3 means a horizontal shift left (negative) 3 spaces.

a - vertical stretch/shrink. Negative a is reflection over x-axis.

b - horizontal shrink/stretch (the opposite) - So if b=3, it's a horizontal shrink of 1/3. If b=1/3, it's a horizontal stretch of 3. Negative b is reflection over y-axis.

Also, we need to be careful because the problem has two parts: horizontal stretch and translation up "followed by" reflection "in" the y-axis.

Using these rules, the transformation for the first part of the problem (horizontal stretch and translation up) is f(1/2 x) + 2 and then we apply this to the function f(x) = 8x² - 6, and get 8(1/2 x)² - 6 +2 = 2x² - 4

Now we do reflection "in" the y-axis. Frankly, I don't know what "in" means.

If it means reflection over the y-axis, then you'd change the x into a -x and get 2(-x)² - 4, which ends up being the same thing 2x² - 4. There is no change because this function is symmetric over the y-axis.

If it means reflection along the y-axis, then you'd put a minus sign in front the whole expression -(2x² - 4), which turns the graph upside down. -32x² + 4.