If f(x) = x ^ 2 is vertically compressed by a factor of 9 to g(x) , what is the equation of g(x) ?

Mathematics

1 answer:

Maslowich3 years ago

6 0

Answer:

$g(x) = \frac{1}{9} \,x^2$ which agrees with option A in the list of possible answers

Step-by-step explanation:

A vertical compression by a factor 9 is represented by the transformation:

$\frac{1}{9} \,f(x) = \frac{1}{9} \,x^2$

Therefore the answer to the problem is:

$g(x) = \frac{1}{9} \,x^2$

You might be interested in

How do you solve the quadratic equation (x-2)^=49

Usimov [2.4K]

Assuming you mean
(x-2)²=49
sqare root both sides and take positive and negative roots
x-2=+/-7
add 2 to both sides
x=2+/-7
x=2+7 and 2-7
x=9 and -5

7 0

2 years ago

Given: △ABC, m∠A=60°, m∠C=45°, AB=9 Find: Perimeter of △ABC, Area of △ABC

stellarik [79]

Answer:

Perimeter of ΔABC: $\frac{27}{2}$ + $\frac{9}{2} * \sqrt6$ units

Area of ΔABC: $\frac{81}{8}*\sqrt3 + \frac{243}{8}$ units

Skills required: HS Geo, Special Triangles

Step-by-step explanation:

1) The best option is to break down this triangle. Let's draw an altitude from Point B down to Segment AC. The point from the altitude that intersects AC is Point D. BD is the height of our triangle, AC is the base.

2) Angle A is 60 degrees, and since Angle BDA is 90 degrees, Angle ABD is 30 degrees. We can use the 30-60-90 degree right triangle property for the triangle BDA.

This states that if the side opposite the 30 degree angle is $x$ , the side opposite the 60 degree angle is $x*\sqrt3$ , and the side opposite the 90 degree angle is $2x$ .

AB is 9 units, and it is opposite the 90 degree angle. This means that $2x=9, x = \frac{9}{2}$ ==> This then means that AD, the segment opposite the 30 degree angle in this triangle is $\frac{9}{2}$ units. Segment BD (the height) is $\frac{9}{2} * \sqrt3$ .

3) Angle C is 45 degrees, and Angle BDC is 90 degrees, which means that Angle CBD is 45 degrees. We can use the 45-45-90 degree right triangle property for the triangle BCD.

This states that if the side opposite the 45 degree angle is $x$ , the other side opposite a 45 degree angle is also $x$ , but the hypotenuse (side opposite the right (90 degree) angle) is $\sqrt{2}*x$ .

BD is $\frac{9}{2} * \sqrt3$ , which means DC is the same. BC, which is the hypotenuse is BD multiplied by square-root-2, which is $\frac{9}{2} * \sqrt6$ .

4) Area is $\frac{1}{2}*b*h$ , the base (b) is AC (which is $\frac{9}{2}+\frac{9}{2}*\sqrt3$ ), the height is BD ( $\frac{9}{2}*\sqrt3$ ). When multiple you will get $\frac{81}{4}*\sqrt3 + \frac{243}{4}$ , then this multiplied by 1/2 is