Which graph represents the function f(x) = |x + 3|? 1. On a coordinate plane, an absolute value graph has a vertex at (0, 3). 2. On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0). 3. On a coordinate plane, an absolute value graph has a vertex at (0, negative 3). 4. On a coordinate plane, an absolute value graph has a vertex at (3, 0).

Question

2. Which graph represents the function r(x) = |x – 2| – 1 1. On a coordinate plane, an absolute value graph has a vertex at (2, negative 1). 2. On a coordinate plane, an absolute value graph has a vertex at (negative 2, negative 1). 3. On a coordinate plane, an absolute value graph has a vertex at (1, negative 2). 4. On a coordinate plane, an absolute value graph has a vertex at (negative 1, negative 2).

3. Which functions have a vertex with a x-value of 0? Select three options.

f(x) = |x|
f(x) = |x| + 3
f(x) = |x + 3|
f(x) = |x| − 6
f(x) = |x + 3| – 6

4. Over which interval is the graph of the parent absolute value function f(x)=|x| decreasing?

(–∞, ∞)
(–∞, 0)
(–6, 0)
(0, ∞)

5. On each coordinate plane, the parent function f(x) = |x| is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g(x) = |x| – 4 as a solid line? 1. On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (0, negative 4). 2. On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (0, 4). 3. On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (4, 0). 4. On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (negative 4, 0).

6. On a coordinate plane, an absolute value graph has a vertex at (1, negative 2.5).The graph shows the function f(x) = |x – h| + k. What is the value of k?
k = –2.5
k = –1
k = 1
k = 2.5

7. On a coordinate plane, an absolute value graph has a vertex at (negative 1.5, negative 3.5).The graph shows the function f(x) = |x – h| + k. What is the value of h?
h = –3.5
h = –1.5
h = 1.5
h = 3.5

8. On a coordinate plane, an absolute value graph has a vertex at (negative 4, negative 10).Which equation represents the function graphed on the coordinate plane?
g(x) = |x – 4| – 10
g(x) = |x + 4| – 10
g(x) = |x – 10| + 4
g(x) = |x + 10| – 4

9. The graph of f(x) = |x| is translated 6 units to the right and 2 units up to form a new function. Which statement about the range of both functions is true?

The range is the same for both functions: {y | y is a real number}.
The range is the same for both functions: {y | y > 0}.
The range changes from {y | y > 0} to {y | y > 2}.
The range changes from {y | y > 0} to {y | y > 6}.

10. On each coordinate plane, the parent function f(x) = |x| is represented by a dashed line and a translation is represented by a solid line. Which graph represents the translation g(x) = |x + 2| as a solid line? 1. On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (2, 0). 2. On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (0, negative 2). 3. On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (negative 2, 0). 4. On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (0, 2).

Answer 1

Let's address each question one by one:

1. Which graph represents the function f(x) = |x + 3|?

   • The function f(x) = |x + 3| translates the parent function |x| to the left by 3 units. Hence, its vertex is at (-3, 0).
   • Answer: 2. On a coordinate plane, an absolute value graph has a vertex at (negative 3, 0).

2. Which graph represents the function r(x) = |x – 2| – 1?

   • The function r(x) = |x – 2| - 1 translates the parent function |x| to the right by 2 units and down by 1 unit. Thus, its vertex is at (2, -1).
   • Answer: 1. On a coordinate plane, an absolute value graph has a vertex at (2, negative 1).

3. Which functions have a vertex with an x-value of 0? (Select three options.)

   • f(x) = |x| has a vertex at (0, 0).
   • f(x) = |x| + 3 has a vertex at (0, 3).
   • f(x) = |x| - 6 has a vertex at (0, -6).
   • Answer:
     • f(x) = |x|
     • f(x) = |x| + 3
     • f(x) = |x| − 6

4. Over which interval is the graph of the parent absolute value function f(x) = |x| decreasing?

   • The parent absolute value function is decreasing on the interval (–∞, 0).
   • Answer: (–∞, 0)

5. Which graph represents the translation g(x) = |x| – 4 as a solid line?

   • The function g(x) = |x| - 4 shifts the graph of |x| down by 4 units, resulting in a vertex at (0, -4).
   • Answer: 1. On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (0, negative 4).

6. What is the value of k if the vertex is at (1, negative 2.5) for f(x) = |x – h| + k?

   • In the vertex form f(x) = |x - h| + k, k represents the y-coordinate of the vertex. Thus, k = -2.5.
   • Answer: k = –2.5

7. What is the value of h if the vertex is at (negative 1.5, negative 3.5) for f(x) = |x – h| + k?

   • In the vertex form f(x) = |x - h| + k, h represents the x-coordinate of the vertex. Thus, h = -1.5.
   • Answer: h = –1.5

8. Which equation represents the function graphed if the vertex is at (negative 4, negative 10)?

   • The vertex at (-4, -10) suggests the function is in the form f(x) = |x + 4| - 10.
   • Answer: g(x) = |x + 4| – 10

9. Which statement about the range of both functions is true after the translation of f(x) = |x|?

   • The function f(x) = |x| has a range of {y | y ≥ 0}, and the translated function will have a range of {y | y ≥ 2} after being moved up by 2 units.
   • Answer: The range changes from {y | y > 0} to {y | y > 2}.

10. Which graph represents the translation g(x) = |x + 2| as a solid line?

    • The function g(x) = |x + 2| translates the graph left by 2 units, resulting in a vertex at (-2, 0).
    • Answer: 3. On a coordinate plane, a dashed line absolute value graph has a vertex at (0, 0). A solid line absolute value graph has a vertex at (negative 2, 0).

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Answer 2

100!!!!

Answer 3

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