Question

!50 POINTS! (3 SIMPLE GEOMETRY QUESTIONS)

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Answer 1

D

Explanation:

Certainly, let's provide a mathematical explanation for the transformation of the function from f(x) to h(x).

The original function is given as:

f(x) = (x + 2)³ - 3

Horizontal Shift: The term "(x + 2)" represents a horizontal shift to the left by 2 units. This means that every point on the graph of f(x) is moved 2 units to the left compared to the standard cubic function.

Cubic Function: The term "³" represents a cubic function. It indicates that the graph is a cubic curve, which has a characteristic shape with a single point of inflection.

Vertical Shift: The term "-3" represents a vertical shift downward by 3 units. This means that the entire graph is shifted downward by 3 units compared to the standard cubic function.

Now, to express h(x) in terms of x, we perform the same transformations on a basic cubic function, which we'll call k(x):

k(x) = x³

To obtain h(x), we apply the same transformations to k(x):

h(x) = k(x + 2) - 3

This expression for h(x) mirrors the transformations applied to the original function f(x). It represents a cubic function that has been shifted 2 units to the left and 3 units down from the standard cubic function.

So, h(x) = (x + 2)³ - 3 is the expression for h(x) that matches the transformations applied to f(x).

Answer 2

1st: b

2nd. b and e

3rd. a

Explanation:

1st question:

The side splitter theorem says that if a line is parallel to one side of a triangle, intersects the other 2 sides then it divides the 2 sides proportionally. The answer that matches this theorem is b.

2nd question:

b. The corresponding sides are similar (CPCTC) (Have a common included angle)

e. The included angles are congruent

3rd question:

A. There are 2 vertical angles (which would be congruent), and we are given 2 congruent angles. Using the 3rd angle theorem we can see that the 2 triangles are similar by AAA similarity.