Q. If a function f is defined as f(x) = 3x + 2, what is the value of f(4)?
Solution
To find f(4), substitute x with 4: f(4) = 3(4) + 2 = 12 + 2 = 14.
Correct Answer: A — 14
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Q. If a function f(x) is defined as f(x) = 2x + 3, what is the slope of the graph?
Solution
In the linear function f(x) = mx + b, 'm' represents the slope. Here, the slope is 2.
Correct Answer: C — 2
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Q. If a function f(x) is defined as f(x) = 2x + 5, what is the slope of the graph?
-
A.
0
-
B.
2
-
C.
5
-
D.
Undefined
Solution
In the linear function f(x) = mx + b, 'm' represents the slope. Here, m = 2.
Correct Answer: B — 2
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Q. If the graph of a function f(x) is symmetric about the y-axis, which of the following must be true?
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A.
f(x) = f(-x) for all x.
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B.
f(x) = -f(-x) for all x.
-
C.
f(x) is always positive.
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D.
f(x) has a maximum value.
Solution
A function that is symmetric about the y-axis satisfies the property f(x) = f(-x) for all x.
Correct Answer: A — f(x) = f(-x) for all x.
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Q. If the graph of a function is symmetric about the y-axis, which of the following types of functions could it be?
-
A.
Linear function
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B.
Odd function
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C.
Even function
-
D.
Exponential function
Solution
A function is symmetric about the y-axis if it is an even function, which satisfies the condition f(x) = f(-x).
Correct Answer: C — Even function
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Q. In a function f(x) = ax^2 + bx + c, what does the coefficient 'a' determine?
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A.
The direction of the parabola's opening.
-
B.
The y-intercept of the graph.
-
C.
The slope of the graph.
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D.
The x-intercepts of the graph.
Solution
The coefficient 'a' in a quadratic function determines whether the parabola opens upwards (a > 0) or downwards (a < 0).
Correct Answer: A — The direction of the parabola's opening.
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Q. In a function f(x) = x^3 - 3x, what is the nature of the critical points?
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A.
All critical points are local maxima.
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B.
All critical points are local minima.
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C.
There are both local maxima and minima.
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D.
There are no critical points.
Solution
The function has critical points where the first derivative is zero, which can be analyzed to find both local maxima and minima.
Correct Answer: C — There are both local maxima and minima.
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Q. In the context of functions and graphs, which of the following statements best describes a linear function?
-
A.
A function that has a constant rate of change and can be represented by a straight line.
-
B.
A function that varies exponentially and is represented by a curve.
-
C.
A function that has multiple outputs for a single input.
-
D.
A function that is defined only for positive integers.
Solution
A linear function is characterized by a constant rate of change, which means that its graph is a straight line.
Correct Answer: A — A function that has a constant rate of change and can be represented by a straight line.
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Q. In the context of functions and graphs, which of the following statements best describes a quadratic function?
-
A.
It is a linear function with a constant slope.
-
B.
It is a polynomial function of degree two.
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C.
It is a function that can only take positive values.
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D.
It is a function that has a single output for every input.
Solution
A quadratic function is defined as a polynomial function of degree two, typically represented in the form f(x) = ax^2 + bx + c.
Correct Answer: B — It is a polynomial function of degree two.
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Q. In the context of functions, what does the term 'asymptote' refer to?
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A.
A line that the graph approaches but never touches.
-
B.
A point where the graph intersects the x-axis.
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C.
A maximum or minimum point on the graph.
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D.
A point of discontinuity in the graph.
Solution
An asymptote is a line that a graph approaches as it heads towards infinity but does not intersect.
Correct Answer: A — A line that the graph approaches but never touches.
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Q. In the context of functions, what does the term 'domain' refer to?
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A.
The set of all possible output values.
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B.
The set of all possible input values.
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C.
The maximum value of the function.
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D.
The minimum value of the function.
Solution
The domain of a function is the set of all possible input values (x-values) for which the function is defined.
Correct Answer: B — The set of all possible input values.
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Q. In the function f(x) = |x|, what is the value of f(-3)?
-
A.
-3
-
B.
0
-
C.
3
-
D.
Undefined
Solution
The absolute value function returns the non-negative value of x, so f(-3) = 3.
Correct Answer: C — 3
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Q. What does the term 'asymptote' refer to in the context of graphing functions?
-
A.
A point where the function intersects the x-axis.
-
B.
A line that the graph approaches but never touches.
-
C.
A maximum point on the graph.
-
D.
A minimum point on the graph.
Solution
An asymptote is a line that a graph approaches as it heads towards infinity, but does not actually touch.
Correct Answer: B — A line that the graph approaches but never touches.
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Q. Which of the following best describes the end behavior of the function f(x) = -x^4?
-
A.
Both ends go to positive infinity.
-
B.
Both ends go to negative infinity.
-
C.
The left end goes to negative infinity and the right end goes to positive infinity.
-
D.
The left end goes to positive infinity and the right end goes to negative infinity.
Solution
Since the leading coefficient is negative and the degree is even, both ends of the graph will go to negative infinity.
Correct Answer: B — Both ends go to negative infinity.
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Q. Which of the following functions has a vertical asymptote?
-
A.
f(x) = x^2 + 1
-
B.
f(x) = 1/(x - 2)
-
C.
f(x) = e^x
-
D.
f(x) = log(x)
Solution
The function f(x) = 1/(x - 2) has a vertical asymptote at x = 2, where the function is undefined.
Correct Answer: B — f(x) = 1/(x - 2)
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Q. Which of the following graphs represents a function that is neither increasing nor decreasing?
-
A.
A straight line with a positive slope
-
B.
A straight line with a negative slope
-
C.
A horizontal line
-
D.
A parabolic curve opening upwards
Solution
A horizontal line represents a function that is constant, meaning it neither increases nor decreases.
Correct Answer: C — A horizontal line
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Q. Which of the following graphs represents a quadratic function?
-
A.
A straight line.
-
B.
A parabola opening upwards or downwards.
-
C.
A hyperbola.
-
D.
A circle.
Solution
A quadratic function is represented by a parabola, which can open either upwards or downwards.
Correct Answer: B — A parabola opening upwards or downwards.
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Q. Which of the following is a characteristic of exponential functions?
-
A.
They have a constant rate of change.
-
B.
They grow or decay at a constant percentage rate.
-
C.
They are always positive.
-
D.
They can be represented by a straight line.
Solution
Exponential functions grow or decay at a constant percentage rate, which is a defining characteristic.
Correct Answer: B — They grow or decay at a constant percentage rate.
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Q. Which of the following statements is true about the graph of a function that is periodic?
-
A.
It repeats its values at regular intervals.
-
B.
It is always increasing.
-
C.
It has no maximum or minimum values.
-
D.
It is a straight line.
Solution
A periodic function is characterized by repeating values at regular intervals, such as sine and cosine functions.
Correct Answer: A — It repeats its values at regular intervals.
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Q. Which of the following statements is true about the inverse of a function?
-
A.
The inverse of a function is always a function.
-
B.
The inverse of a function is not necessarily a function.
-
C.
The inverse of a function is always linear.
-
D.
The inverse of a function cannot be graphed.
Solution
The inverse of a function is a function only if the original function is one-to-one.
Correct Answer: B — The inverse of a function is not necessarily a function.
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