Answers NY-Algebra I Term 2 HillcrestAnalyzing Functional Relationships

Analyzing Functional Relationships — Unit test Answers

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The length of time in hours of two airplane flights are represented by the following functions, where x is the number of miles for the flight:Flight A: f(x) = 0.003x – 1.2Flight B: g(x) = 0.0015x + 0.8Which function represents the total of the flight times, h(x) = f(x) + g(x)?

h(x) = 0.0015x – 2

h(x) = 0.045x – 0.4

h(x) = 0.0045x – 0.4

h(x) = 0.0045x – 2

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A vitamin degrades in the body according to the function represented in the table, where x is the time in hours and f(x) is the dosage in milligrams.

0.50 milligrams

8 milligrams

24 milligrams

500 milligrams

The graph of the function f(x) = –(x + 3)(x – 1) is shown below.

The domain is all real numbers less than or equal to 4, and the range is all real numbers such that –3 ≤ x ≤ 1.

The domain is all real numbers such that –3 ≤ x ≤ 1, and the range is all real numbers less than or equal to 4.

The domain is all real numbers, and the range is all real numbers less than or equal to 4.

The domain is all real numbers less than or equal to 4, and the range is all real numbers.

Which is one of the transformations applied to the graph of f(x) = x2 to change it into the graph of g(x) = 4x2 + 24x + 30?

The graph of f(x) = x2 is widened.

The graph of f(x) = x2 is shifted left 3 units.

The graph of f(x) = x2 is shifted up 30 units.

The graph of f(x) = x2 is reflected over the x-axis.

Which function in vertex form is equivalent to f(x) = x2 + x +1?

f(x) = +

f(x) = +

f(x) = +

f(x) = +

The first steps in writing f(x) = 4x2 + 48x + 10 in vertex form are shown.f(x) = 4(x2 + 12x) + 10 = 36

f(x) = 4(x + 6)2 + 10

f(x) = 4(x + 6)2 – 26

f(x) = 4(x + 6)2 – 134

f(x) = 4(x + 6)2 + 154

The graph is a two-dimensional representation of the curve a manufacturer uses to define the shape of a commercial satellite in feet.

4 ft

6 ft

8 ft

12 ft

Which graph represents the function f(x) = –x2 + 5?

On a coordinate plane, a parabola opens down. It goes through (negative 3, negative 4), has a vertex at (0, 5), and goes through (3, negative 4).

On a coordinate plane, a parabola opens up. It goes through (negative 2, 9), has a vertex at (0, 5), and goes through (2, 9).

On a coordinate plane, a parabola opens down. It goes through (negative 6, negative 9), has a vertex at (negative 5, 0), and goes through (negative 2, negative 9).

On a coordinate plane, a parabola opens up. It goes through (negative 8, 9), has a vertex at (negative 5, 0), and goes through (negative 2, 10).

Ajay analyzed two companies and has formulated tables to model each company’s growth, where x represents the age of the companies in years and y represents growth in terms of number of employees. Company 1 Company 2 If the number of employees is an indicator of a successful business, in which company should Ajay invest?

company 1 because it is adding six employees each year while company 2 is multiplying its number of employees by six each year

company 1 because it is multiplying its number of employees by six each year while company 2 is adding six employees each year

company 2 because it is adding six employees each year while company 1 is multiplying its number of employees by six each year

company 2 because it is multiplying its number of employees by six each year while company 1 is adding six employees each year

An algebra tile configuration. Only the Product spot is shown. 8 tiles are in the Product spot in 3 columns with 3 rows. First row: 1 + x squared, 2 + x. Second row: 1 +x, 2 +. Third row: 1 +x, 1 +.

Which of the following describes the growth rate of the exponential function in the graph below?

For each x increase of 1, the y increases by a common difference of 3.

For each x increase of 1, the y increases by a common factor of 3.

For each x increase of 1, the y increases by 4 more than the previous increase.

For each x increase of 1, the y increases by doubling and then adding 1.

Which is the graph of f(x) = x2 – 2x + 3?

On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (1, 2), and goes through (2, 3).

On a coordinate plane, a parabola opens up. It goes through (negative 2, 3), has a vertex at (negative 1, 2), and goes through (0, 3).

On a coordinate plane, a parabola opens up. It goes through (0, 3), has a vertex at (2, negative 1), and goes through (4, 3).

On a coordinate plane, a parabola opens up. It goes through (negative 4, 3), has a vertex at (negative 2, negative 1), and goes through (0, 3).

What is the vertex of the graph of the function f(x) = x2 + 8x − 2 ?

(−4, 18)

(0, -2)

(-8, -2)

(−4, −18)

Which point is an x-intercept of the quadratic functionf(x) = (x – 8)(x + 9)?

(0,8)

(0,–8)

(9,0)

(–9,0)

Study the equations:f(x) = 6x + 7g(x) = 4x – 2What is h(x) = f(x)g(x)?

h(x) = 24x2 – 14

h(x) = 24x2 + 40x + 14

h(x) = 24x2 + 16x – 14

h(x) = 24x2 + 12x – 14

Given the function f(x) = −5x2 − x + 20, find f(3).

−28

−13

Which quadratic function is the standard form of the equation shown?f(x) = x + 8 + 2x + 5x2

f(x) = 8 + 5x2 + 2x + x

f(x) = x + 2x + 5x2 + 8

f(x) = 8 + 3x + 5x2

f(x) = 5x2 + 3x + 8

Which function has an axis of symmetry of x = −2?

f(x) = (x − 1)2 + 2

f(x) = (x + 1)2 − 2

f(x) = (x − 2)2 − 1

f(x) = (x + 2)2 − 1

The first three steps in writing f(x) = 40x + 5x2 in vertex form are shown.Write the function in standard form.f(x) = 5x2 + 40xFactor a out of the first two terms.f(x) = 5(x2 + 8x)Form a perfect square trinomial. = 16 f(x) = 5(x2 + 8x + 16) – 5(16)What is the function written in vertex form?