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3 years ago

Given the parent function f(x)=x^2 in red, write the equation for the transformed function g(x) in green.

Mathematics

1 answer:

Nataly_w [17]3 years ago

5 0

Answer:

g(x) = 2x² + 1

Step-by-step explanation:

The parabola got thinner, so to show that, you put a 2 before x² to show that the graph was dilated (or thinned) by a factor of 2 (Note: this number can also be negative, so if the dilation factor is negative, it's okay). Since the parabola shifts up by 1, you then add + 1 after x² to show the positive upward shift.

Your full equation would look like this: g(x) = 2x² + 1

Dilation: this just means that every point on the parent function was double (or whatever the factor is) in the transformed function.

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Consider the system of equations.

Harman [31]

The solution to the system of equations x + 2y = 1 and -3x-2y = 5 is:

x = -3, y = 2

The given system of equations:

x + 2y = 1............(1)

-3x - 2y = 5..........(2)

This can be written in matrix form as shown:

$\left[\begin{array}{ccc}1&2\\-3&-2\end{array}\right] \left[\begin{array}{ccc}x\\y\end{array}\right] = \left[\begin{array}{ccc}1\\5\end{array}\right]$

Find the determinant of $\left[\begin{array}{ccc}1&2\\-3&-2\end{array}\right]$

$\triangle = 1(-2) - 2(-3)\\\triangle = -2+6\\\triangle = 4$

$\triangle_x = \left[\begin{array}{ccc}1&2\\5&-2\end{array}\right]\\\triangle_x = 1(-2)-2(5)\\\triangle_x = -2-10\\\triangle_x =-12$

$\triangle_y = \left[\begin{array}{ccc}1&1\\-3&5\end{array}\right]\\\triangle_y = 1(5)-1(-3)\\\triangle_y = 5 + 3\\\triangle_y =8$

$x = \frac{\triangle_x}{\triangle} \\x = \frac{-12}{4} \\x = -3$

$y = \frac{\triangle_y}{\triangle} \\y = \frac{8}{4} \\y = 2$

The solution to the system of equations x + 2y = 1 and -3x-2y = 5 is:

x = -3, y = 2

Learn more here: brainly.com/question/4428059

3 0

2 years ago

A function is blank a relation *always *sometimes *never

zvonat [6]

Answer:

The correct answer is A.) Always

Step-by-step explanation:

A function is defined as a relation in which each element of the domain is mapped to one element of the range. In the definition itself, it is defined as a relation

I hope this helps you :)

-KeairaDickson

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3 years ago

Help I really need help

mylen [45]

Ok well I will send it you your phone number I can text

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3 years ago

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