Math Test 3
D- ✅✅ -The graph of which of the following basic functions is increasing on the
interval (-∞,∞)?
A. f(x)=1/x
B. f(x)=|x|
C. f(x)=x^2
D. f(x)=∛x
A- ✅✅ -Identify the collection of three functions whose graphs are all symmetric
about the origin.
A. y=1/x, y=x, and y∛x
B. y=x^3, y=3, and y=1/x
C. y=|x|, y=1/x, and y=x^3
D. y=x^3, y=x^2, and y=√x
B- ✅✅-Identify the collection of three functions that are all even.
A. y=x, y=x^2, and y=y=1/x, y=x, and y=√x
B. y=-3, y=x^2, and y=|x|
C. y=|x|, y=√x, and y=2
D. y=x^2, y=3, and y=1/x
D- ✅✅ -Which of the following basic functions is equivalent to the
piece-wise-defined function
f(x){ x if x≥0
-x if x<0 ?
A. f(x)=1/x
B. f(x)=x^2
C. f(x)=x
, D. f(x)=|x|
A- ✅✅-Which of the following statements is not true?
A. It is possible for a piecewise-defined function to have more than one y-intercept
depending on how the function is defined.
B. Given that the graph of piecewise-defined function, it is sometimes possible to find
a rule that describes the graph.
C. The range of a piecewise-defined function can be (-∞,∞).
D. The domain of a piecewise-defined function can be (-∞,∞).
C- ✅✅ -Given the graph of y=f(x), if c is a positive real number, then which of the
following statements best describes how to sketch the graph of y=f(x)+c?
A. The graph of y=f(x)+c can be obtained by horizontally shifting the graph of y=f(x)
to the right c units.
B. The graph of y=f(x)+c can be obtained by vertically shifting the graph of y=f(x)
down c units.
C. The graph of y=f(x)+c can be obtained by vertically shifting the graph of y=f(x) up
c units.
D. The graph of y=f(x)+c can be obtained by horizontally shifting the graph of y=f(x)
to the left c units.
D- ✅✅ -Given the graph of y=f(x), if c is a positive real number, then which of the
following statements best describes how to sketch the graph of y=f(x+c)?
A. The graph of y=f(x+c) can be obtained by vertically shifting the graph of y=f(x) up
c units.
B. The graph of y=f(x+c) can be obtained by horizontally shifting the graph of y=f(x)
to the right c units.
C. The graph of y=f(x+c) can be obtained by vertically shifting the graph of y=f(x)
down c units.
D. The graph of y=f(x+c) can be obtained by horizontally shifting the graph of y=f(x)
to the left c units.
D- ✅✅ -The graph of which of the following basic functions is increasing on the
interval (-∞,∞)?
A. f(x)=1/x
B. f(x)=|x|
C. f(x)=x^2
D. f(x)=∛x
A- ✅✅ -Identify the collection of three functions whose graphs are all symmetric
about the origin.
A. y=1/x, y=x, and y∛x
B. y=x^3, y=3, and y=1/x
C. y=|x|, y=1/x, and y=x^3
D. y=x^3, y=x^2, and y=√x
B- ✅✅-Identify the collection of three functions that are all even.
A. y=x, y=x^2, and y=y=1/x, y=x, and y=√x
B. y=-3, y=x^2, and y=|x|
C. y=|x|, y=√x, and y=2
D. y=x^2, y=3, and y=1/x
D- ✅✅ -Which of the following basic functions is equivalent to the
piece-wise-defined function
f(x){ x if x≥0
-x if x<0 ?
A. f(x)=1/x
B. f(x)=x^2
C. f(x)=x
, D. f(x)=|x|
A- ✅✅-Which of the following statements is not true?
A. It is possible for a piecewise-defined function to have more than one y-intercept
depending on how the function is defined.
B. Given that the graph of piecewise-defined function, it is sometimes possible to find
a rule that describes the graph.
C. The range of a piecewise-defined function can be (-∞,∞).
D. The domain of a piecewise-defined function can be (-∞,∞).
C- ✅✅ -Given the graph of y=f(x), if c is a positive real number, then which of the
following statements best describes how to sketch the graph of y=f(x)+c?
A. The graph of y=f(x)+c can be obtained by horizontally shifting the graph of y=f(x)
to the right c units.
B. The graph of y=f(x)+c can be obtained by vertically shifting the graph of y=f(x)
down c units.
C. The graph of y=f(x)+c can be obtained by vertically shifting the graph of y=f(x) up
c units.
D. The graph of y=f(x)+c can be obtained by horizontally shifting the graph of y=f(x)
to the left c units.
D- ✅✅ -Given the graph of y=f(x), if c is a positive real number, then which of the
following statements best describes how to sketch the graph of y=f(x+c)?
A. The graph of y=f(x+c) can be obtained by vertically shifting the graph of y=f(x) up
c units.
B. The graph of y=f(x+c) can be obtained by horizontally shifting the graph of y=f(x)
to the right c units.
C. The graph of y=f(x+c) can be obtained by vertically shifting the graph of y=f(x)
down c units.
D. The graph of y=f(x+c) can be obtained by horizontally shifting the graph of y=f(x)
to the left c units.
