The function f(x) = x2 - 6x + 9 is shifted 5 units to the left to create g(x). What is g(x)?

Mathematics

1 answer:

creativ13 [48]3 years ago

3 0

Answer:

g(x) = x^2 + 4x + 4

Step-by-step explanation:

In translation of functions, adding a constant to the domain values (x) of a function will move the graph to the left, while subtracting from the input of the function will move the graph to the right.

Given the function;

f(x) = x2 - 6x + 9

a shift 5 units to the left implies that we shall be adding the constant 5 to the x values of the function;

g(x) = f(x+5)

g(x) = (x+5)^2 - 6(x+5) + 9

g(x) = x^2 + 10x + 25 - 6x -30 + 9

g(x) = x^2 + 4x + 4

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What is the solution to the system of equations? ⎧⎩⎨⎪⎪x+3y−z=24x+2y+5z=13x+z=12 (−4, 1, −3) (3, 0, 3) (5, −2, −3) (−1, 2, 3)

snow_tiger [21]

<h3>Answer:</h3>

(5, -2, -3)

<h3>Explanation:</h3>

We assume your equations are ...

x +3y -z = 2
4x +2y +5z = 1
3x +0y +z = 12

These have solution (x, y, z) = (5, -2, -3).

_____

Trying the choices in the last equation eliminates the first and last. Trying the second choice in the first equation eliminates it, leaving the 3rd choice as the answer you're looking for.

We also know because we can ask a graphing calculator to solve the matrix equation (or row-reduce the augmented matrix).

<em>Comment on this problem</em>

The hardest part of this problem is figuring your intent. The equations are not well-separated, so we have a hard time telling what is a constant and what is a coefficient. It took a couple of guesses to sort it out. A little editing before posting would be helpful.