Optimization
Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.
Integration
Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.
Application of Integration
In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.
Volume
In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).
Area
Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.
![_18 If the common ratio in a table of values is 3, what exponential function can be derived
from this?
a) f(x) = 3*
b) f(x) = x³
c) f(x) = 3x
d) f(x) = 33x
_19 Suppose that you test apple juice and find that the hydrogen ion concentration is [H*]
= 0.0003. Find the pH value and determine whether the juice is basic or acidic.
pH = -log(H']
a) The pH value is 1.52 therefore it is
basic.
c) The pH value is 3.52 therefore it is
basic.
d) The pH value is 3.52 therefore it is
b) The pH value is 1.52 therefore it is
acidic.
acidic.
_20 Given an exponential function f(x) = 2*, what do you think will happen to the graph if
the range values are increasing?
a) The graph will stretch upward following a straight path.
b) The graph will stretch upward passing through y = 1 following a straight path.
c) The graph will stretch upward passing through y = 1 following an increasing
trend in x.
d) The graph will stretch upward passing through x = 1.
_21 If y = )* and y = 2* are functions and sketched on the same plane, which
description is TRUE with respect to y axis?
a) Both graphs will pass through y
axis at two distinct points.
b) Both graphs will pass through
y = -1.
_22 Study the table of values, what exponential function is represented by the points?
c) The two graphs will be
asymptotic to y - axis.
d) The two graphs are symmetric
over the y - axis.
X0 123
|y 2 48 16
a) f(x) = 2x?
b) f(x) = 2x*+1
c) f(x) = 2*+1
d) f(x) = (x+1)2
_23 What is the value of x in logs(x-+4x+4)=2?
a) x = 7, x = -3
b) x = -7, x = 3
c) x = -7
d) x = 3
_24 What is the range of f(x) = 2*?
a) All real numbers.
b) All real numbers except 2.
c) All real numbers greater than 1.
d) All real numbers greater than 2.
_25 What is the y intercept of f(x) = 3*1?
a) 1
b) 3
2
c)
3
d) -3
_26 If x = 0, what value will yield f(x) = 3*+1?
a) 1
b) 3
c)
d) -3
_27 Given f(x) = (*, which would give a greater y value, x = 1 or x = -1?
a) None. The two y values would be
equal.
b) None. The two y values could not
be defined.
c) The y value for f(1) is greater
than f(-1).
d) The y value for f(-1) is greater
than f(1).
_28 Express 32 = 2* into a logarithmic equation.
a) log 32 = x
b) log32 = 2x
c) log2 32 = x
d) log2 x = 32](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0519d2b5-d9fc-4ec0-aef7-e442abb4add6%2F72973680-9585-478c-b8ec-fc53a5cda6bd%2Famcubki_processed.jpeg&w=3840&q=75)
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