Question

f(x)=4x^2-3 translate to g(x)

Answer 1

[AI-generated answer — Bot GPT 3.5]

To translate the function f(x) = 4x^2 - 3, we can shift the graph horizontally or vertically.

If we want to shift the graph horizontally, we can use the equation g(x) = f(x - h), where h represents the amount of horizontal shift.

If we want to shift the graph vertically, we can use the equation g(x) = f(x) + k, where k represents the amount of vertical shift.

Let's say we want to shift the graph 3 units to the right. We will use g(x) = f(x - 3). Plugging in f(x) = 4x^2 - 3 into this equation, we get:

g(x) = 4(x - 3)^2 - 3

This represents the translated function g(x) that has been shifted 3 units to the right.

Similarly, let's say we want to shift the graph 5 units upward. We will use g(x) = f(x) + 5. Plugging in f(x) = 4x^2 - 3 into this equation, we get:

g(x) = 4x^2 - 3 + 5
= 4x^2 + 2

This represents the translated function g(x) that has been shifted 5 units upward.