what is move to the left by 3 of g(x)= 2x^4
To move the graph of g(x) = 2x^4 to the left by 3 units, you would need to replace x with (x + 3) in the equation. This can be expressed as g(x) = 2(x + 3)^4.
To move the function g(x)=2x^4 to the left by 3 units, you can apply a horizontal translation.
To perform this translation, you need to subtract 3 from the x-coordinate of each point on the graph. Here is the step-by-step process:
1. Start with the original function g(x) = 2x^4.
2. Replace x with (x - 3) in the function to shift it to the left by 3 units. The new function becomes g(x - 3) = 2(x - 3)^4.
3. Simplify the expression (x - 3)^4 by expanding it.
4. Multiply the expanded expression by 2 to get the final function.
Therefore, the function g(x) = 2x^4 moved to the left by 3 units is given by g(x - 3) = 2(x - 3)^4.
To move the graph of a function to the left by a certain distance, you can replace the "x" variable in the function with "(x + k)", where "k" represents the distance of the leftward shift.
In this case, we want to move the graph of g(x) = 2x^4 to the left by 3 units.
To achieve this, we replace "x" with "(x + 3)" in the original function:
g(x) = 2(x + 3)^4
Now, let's simplify this expression:
1. Apply the binomial expansion to {(x + 3)^4} using the exponent rule:
(x + 3)^4 = (x + 3)(x + 3)(x + 3)(x + 3)
2. Multiply each term together:
(x + 3)(x + 3) = x^2 + 6x + 9
(x^2 + 6x + 9)(x + 3) = x^3 + 9x^2 + 27x + 27
(x^3 + 9x^2 + 27x + 27)(x + 3) = x^4 + 12x^3 + 54x^2 + 81x + 81
3. Substitute the simplified expression back into the original function:
g(x) = 2(x + 3)^4
g(x) = 2(x^4 + 12x^3 + 54x^2 + 81x + 81)
So, the new function that represents g(x) moved to the left by 3 units is g(x) = 2x^4 + 12x^3 + 54x^2 + 81x + 81.