Question

Explain how the graph of the function f left parenthesis x right parenthesis equals StartFraction 14 Over x EndFraction
can be obtained from the graph of yequalsStartFraction 1 Over x EndFraction
. Then graph f and give the​ (a) domain and​ (b) range. Determine the largest open intervals of the domain over which the function is​ (c) increasing or​ (d) decreasing.
Question content area bottom
Part 1
To obtain the graph of​ f,
▼
shrink
stretch
the graph of yequalsStartFraction 1 Over x EndFraction

▼
vertically
horizontally
by a factor of
  
enter your response here.
Part 2
Graph the function f left parenthesis x right parenthesis equals StartFraction 14 Over x EndFraction
. Choose the correct graph below.
A.
-16
16
-16
16
x
y



A coordinate system has a horizontal x-axis labeled from negative 16 to 16 in increments of 2 and a vertical y-axis labeled from negative 16 to 16 in increments of 2. A graph has two branches. The first branch is above the x-axis and to the left of the y-axis, approaching both and passing through the point (negative 1, 1). The second branch is below the x-axis and to the right of the y-axis, approaching both and passing through the point (1, negative 1).
B.
-16
16
-16
16
x
y



A coordinate system has a horizontal x-axis labeled from negative 16 to 16 in increments of 2 and a vertical y-axis labeled from negative 16 to 16 in increments of 2. A graph has two branches. The first branch is above the x-axis and to the left of the y-axis, approaching both and passing through the point (negative 14, 1). The second branch is below the x-axis and to the right of the y-axis, approaching both and passing through the point (14, negative 1).
C.
-16
16
-16
16
x
y



A coordinate system has a horizontal x-axis labeled from negative 16 to 16 in increments of 2 and a vertical y-axis labeled from negative 16 to 16 in increments of 2. A graph has two branches. The first branch is below the x-axis and to the left of the y-axis, approaching both and passing through the point (negative 1, negative 1). The second branch is above the x-axis and to the right of the y-axis, approaching both and passing through the point (1, 1).
D.
-16
16
-16
16
x
y



A coordinate system has a horizontal x-axis labeled from negative 16 to 16 in increments of 2 and a vertical y-axis labeled from negative 16 to 16 in increments of 2. A graph has two branches. The first branch is below the x-axis and to the left of the y-axis, approaching both and passing through the point (negative 14, negative 1). The second branch is above the x-axis and to the right of the y-axis, approaching both and passing through the point (14, 1).
Part 3
​(a) The domain of​ f(x) is
  
enter your response here.
​(Type your answer in interval​ notation.)
Part 4
​(b) The range of​ f(x) is
  
enter your response here.
​(Type your answer in interval​ notation.)
Part 5
​(c) Determine the largest open intervals of the domain over which the function is increasing. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The function is increasing on
  
enter your response here.
​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)
B.
There is no interval of the domain for which the function is increasing.
Part 6
​(d) Determine the largest open intervals of the domain over which the function is decreasing. Select the correct choice below​ and, if​ necessary, fill in the answer box to complete your choice.
A.
The function is decreasing on
  
enter your response here.
​(Type your answer in interval notation. Use a comma to separate answers as​ needed.)
B.
There is no interval of the domain for which the function is decreasing.
To obtain the graph of f,StartFraction 1 Over x EndFractionthe graph of yStartFraction 1 Over x EndFractionby a factor ofby a factor of.Choose the correct graph below.(a) The domain of f(x) is(Type your answer in interval notation.)(b) The range of f(x) is(Type your answer in interval notation.))Select the correct choice below and, if necessary, fill in the answer box to complete your choice.input field 5Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

Answer 1

f(x) = 14/x = 14·(1/x), so its graph is the graph of y = 1/x stretched vertically by a factor of 14 (horizontal and vertical asymptotes remain x = 0 and y = 0).

Correct graph: D.

(a) Domain: (-∞, 0) ∪ (0, ∞)

(b) Range: (-∞, 0) ∪ (0, ∞)

(c) Increasing: none (there is no interval of the domain where f is increasing).

(d) Decreasing: f is decreasing on (-∞, 0) and on (0, ∞). (f ′(x) = −14/x^2 < 0 for all x ≠ 0.)