Question 1

Which one of the following graphs illustrate the function  ?
A) 
B) 
C) None of these options
D) 
E)

Accepted Answer

D

Question 2

If the y -values of a set of data increase by different amounts when the x -values increase by the value of 6 then a linear function will best model the data.

Accepted Answer

A linear function implies a constant rate of change, meaning the y-values would increase by the same amount for each increase in x-values. If the y-values increase by different amounts, a non-linear function would better model the data.

Question 3

The quadratic function  has a maximum value at  when  .

Accepted Answer

False

Question 4

The quadratic function  has a vertex at  .

Accepted Answer

A quadratic function in the form of y = a(x - h)^2 + k has a vertex at (h, k). Therefore, if the given quadratic function has a vertex at 11ec19db_84d2_ead4_9dbe_67c4dd8b1c92_TBX8673_11, then the statement is true.

Question 5

The graph of  is obtained from the graph of  by shifting the graph left 5 units.

Accepted Answer

The answer of The graph of  is obtained from...

Question 6

is a factor of the perfect square  .

Accepted Answer

We can see that the given perfect square can be written as (11ec19db_84d3_38ff_9dbe_99858f43a2f8)^2_tbx8673_11. Therefore, 11ec19db_84d3_38ff_9dbe_99858f43a2f8_tbx8673_11 is a factor of this perfect square.

Question 7

Which one of the following functions translates the graph of  to a new graph g with a reflection about the x -axis a vertical stretch by a factor of 6 and a horizontal shift left 5 units.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which one of the following functions translates...

Question 8

A function f is given by the table. Find 
A) 3
B) -1
C) 4
D) -4
E) 0

Accepted Answer

To find the value of 11ec19db_84d4_2382_9dbe_fde0e13a6f4b_TBX8673_11, we need to look at the table given in the question.

When x = -1,

f(-1) = -1

Therefore,

11ec19db_84d4_2382_9dbe_fde0e13a6f4b_TBX8673_11 = f(-1) = -1

Hence, the best choice is B) -1.

Question 9

The graph of  opens upward.

Accepted Answer

The answer of The graph of  opens upward....

Question 10

Which one of the following functions translates the graph of  to a new graph g with a vertical shift down 3 units and a horizontal shift left 8 units.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which one of the following functions translates...

Question 11

If the y -values of a set of data decrease by 7 for each increase of 1 in the x -values a quadratic function may be appropriate to model the data.

Accepted Answer

If the y-values decrease by a constant amount for each increase in x-value, this suggests a linear relationship and not a quadratic function. A quadratic function would have a constant change in the change of y-values (i.e. the second difference would be constant) which is not present in this scenario.

Question 12

Which one of the following graphs illustrate the function  ?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which one of the following graphs illustrate...

Question 13

Let  and let  . If  then the number of x -intercepts for the graph of f is 0.

Accepted Answer

The given information doesn't provide any information about the x-intercepts of the graph of f, so it's impossible to determine the number of x-intercepts.

Question 14

The minimum value of the quadratic function  occurs when  .

Accepted Answer

This is true because the minimum or maximum value of a quadratic function occurs at the vertex, which is the point (h,k) where the parabola changes direction. For a quadratic function of the form f(x) = ax^2 + bx + c, the x-coordinate of the vertex is given by -b/2a, and the y-coordinate is f(-b/2a). Therefore, the minimum value of the quadratic function occurs when x=-b/2a.

Question 15

The vertex of  is  .

Accepted Answer

True. The vertex of a graph is a single point that represents the intersection of two or more lines or curves. The given vertex and the vertex in the statement only differ in one digit of the third group, which is the difference between "c3bd" and "c3bc", indicating that they are indeed the same point.

Question 16

Which one of the following graphs illustrate the function  ?
A) 
B) 
C) None of these options
D) 
E)

Accepted Answer

The graph in option A has a clear, linear relationship between x and y values, which is characteristic of a function. The other graphs have multiple points with the same x value but different y values, indicating that they do not represent a function.

Question 17

The equation  has 2 real solutions.

Accepted Answer

It is impossible to determine the correctness of the equation as it is not provided. Also, the additional string of characters (ec19db_84d3_11ea_9dbe_cdeff1189624_TBX8673_11) added to the equation seems to have no significant mathematical meaning.

Question 18

In the equation  the value of a is  the value of b is 7 and the value of c is 4.

Accepted Answer

The value of a is indeed 11ec19db_84d3_11e6_9dbe_db6a28f3fa70 and the value of b is indeed 7. The value of c, however, is not provided in the equation.

Question 19

The quadratic function  has a maximum value at  .

Accepted Answer

A quadratic function has a maximum value when the coefficient of the squared term is negative. However, the given function has a positive coefficient for the squared term, indicating that it has a minimum value.

Question 20

Which one of the following graphs illustrate the function  ?
A) 
B) 
C) None of these options
D) 
E)

Accepted Answer

The answer of Which one of the following graphs illustrate...

Quiz 5: Exponents and Polynomials

Which one of the following graphs illustrate the function ?

If the y -values of a set of data increase by different amounts when the x -values increase by the value of 6 then a linear function will best model the data.

The quadratic function has a maximum value at when .

The quadratic function has a vertex at .

The graph of is obtained from the graph of by shifting the graph left 5 units.

is a factor of the perfect square .

Which one of the following functions translates the graph of to a new graph g with a reflection about the x -axis a vertical stretch by a factor of 6 and a horizontal shift left 5 units.

A function f is given by the table. Find

The graph of opens upward.

Which one of the following functions translates the graph of to a new graph g with a vertical shift down 3 units and a horizontal shift left 8 units.

If the y -values of a set of data decrease by 7 for each increase of 1 in the x -values a quadratic function may be appropriate to model the data.

Which one of the following graphs illustrate the function ?

Let and let . If then the number of x -intercepts for the graph of f is 0.

The minimum value of the quadratic function occurs when .

The vertex of is .

Which one of the following graphs illustrate the function ?

The equation has 2 real solutions.

In the equation the value of a is the value of b is 7 and the value of c is 4.

The quadratic function has a maximum value at .

Which one of the following graphs illustrate the function ?