Question
Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the function equations to their graphs.
f(x) = -|2(x + 5)| − 1
g(x) = |2(x + 5)| − 1
h(x) = 2|x − 5| − 1
k(x) = -2|x − 5| − 1
m(x) = -2|x − 1| − 5
n(x) = 2|x + 1| − 5
A v-shaped acute angled curve joining at (negative 5, positive 1) facing downwards is graphed in a coordinate plane.
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A v-shaped acute angled curve joining at (5, negative 1) facing downwards is graphed in a coordinate plane.
arrowRight
A v-shaped acute angled curve joining at (negative 5, negative 1) facing upwards is graphed in a coordinate plane.
arrowRight
A v-shaped acute angled curve joining at (5, negative 1) facing upwards is graphed in a coordinate plane.
Match the function equations to their graphs.
f(x) = -|2(x + 5)| − 1
g(x) = |2(x + 5)| − 1
h(x) = 2|x − 5| − 1
k(x) = -2|x − 5| − 1
m(x) = -2|x − 1| − 5
n(x) = 2|x + 1| − 5
A v-shaped acute angled curve joining at (negative 5, positive 1) facing downwards is graphed in a coordinate plane.
arrowRight
A v-shaped acute angled curve joining at (5, negative 1) facing downwards is graphed in a coordinate plane.
arrowRight
A v-shaped acute angled curve joining at (negative 5, negative 1) facing upwards is graphed in a coordinate plane.
arrowRight
A v-shaped acute angled curve joining at (5, negative 1) facing upwards is graphed in a coordinate plane.
Answers
GPT-4o mini
To match the function equations to their corresponding graphs, we need to analyze each function and determine its vertex and direction (upward or downward facing).
1. **f(x) = -|2(x + 5)| - 1**
- This equation has a vertex at (-5, -1) and opens downwards (because of the negative sign in front of the absolute value).
- **Graph: A v-shaped acute angled curve joining at (negative 5, negative 1) facing downwards.**
2. **g(x) = |2(x + 5)| - 1**
- This equation has a vertex at (-5, -1) and opens upwards (because there is no negative sign in front of the absolute value).
- **Graph: A v-shaped acute angled curve joining at (negative 5, negative 1) facing upwards.**
3. **h(x) = 2|x - 5| - 1**
- This equation has a vertex at (5, -1) and opens upwards (because of the positive coefficient of the absolute value).
- **Graph: A v-shaped acute angled curve joining at (5, negative 1) facing upwards.**
4. **k(x) = -2|x - 5| - 1**
- This equation has a vertex at (5, -1) and opens downwards (because of the negative sign in front of the absolute value).
- **Graph: A v-shaped acute angled curve joining at (5, negative 1) facing downwards.**
5. **m(x) = -2|x - 1| - 5**
- This equation has a vertex at (1, -5) and opens downwards (because of the negative sign).
- Not mentioned as part of the graphs.
6. **n(x) = 2|x + 1| - 5**
- This equation has a vertex at (-1, -5) and opens upwards.
- Not mentioned as part of the graphs.
Now, let's summarize the matches:
- Function **f(x)**: A v-shaped acute angled curve joining at (negative 5, negative 1) facing downwards.
- Function **g(x)**: A v-shaped acute angled curve joining at (negative 5, negative 1) facing upwards.
- Function **h(x)**: A v-shaped acute angled curve joining at (5, negative 1) facing upwards.
- Function **k(x)**: A v-shaped acute angled curve joining at (5, negative 1) facing downwards.
Given these analyses, the following pairs can be completed:
1. **f(x) with Graph: A v-shaped acute angled curve joining at (negative 5, negative 1) facing downwards.**
2. **h(x) with Graph: A v-shaped acute angled curve joining at (5, negative 1) facing upwards.**
3. **k(x) with Graph: A v-shaped acute angled curve joining at (5, negative 1) facing downwards.**
4. **g(x) with Graph: A v-shaped acute angled curve joining at (negative 5, positive 1) facing upwards.**
Note: Not all functions will match with the graphs provided in the description as per the equations shared. The functions m(x) and n(x) are not used in the matches above since their descriptions were not part of the graph options provided.
1. **f(x) = -|2(x + 5)| - 1**
- This equation has a vertex at (-5, -1) and opens downwards (because of the negative sign in front of the absolute value).
- **Graph: A v-shaped acute angled curve joining at (negative 5, negative 1) facing downwards.**
2. **g(x) = |2(x + 5)| - 1**
- This equation has a vertex at (-5, -1) and opens upwards (because there is no negative sign in front of the absolute value).
- **Graph: A v-shaped acute angled curve joining at (negative 5, negative 1) facing upwards.**
3. **h(x) = 2|x - 5| - 1**
- This equation has a vertex at (5, -1) and opens upwards (because of the positive coefficient of the absolute value).
- **Graph: A v-shaped acute angled curve joining at (5, negative 1) facing upwards.**
4. **k(x) = -2|x - 5| - 1**
- This equation has a vertex at (5, -1) and opens downwards (because of the negative sign in front of the absolute value).
- **Graph: A v-shaped acute angled curve joining at (5, negative 1) facing downwards.**
5. **m(x) = -2|x - 1| - 5**
- This equation has a vertex at (1, -5) and opens downwards (because of the negative sign).
- Not mentioned as part of the graphs.
6. **n(x) = 2|x + 1| - 5**
- This equation has a vertex at (-1, -5) and opens upwards.
- Not mentioned as part of the graphs.
Now, let's summarize the matches:
- Function **f(x)**: A v-shaped acute angled curve joining at (negative 5, negative 1) facing downwards.
- Function **g(x)**: A v-shaped acute angled curve joining at (negative 5, negative 1) facing upwards.
- Function **h(x)**: A v-shaped acute angled curve joining at (5, negative 1) facing upwards.
- Function **k(x)**: A v-shaped acute angled curve joining at (5, negative 1) facing downwards.
Given these analyses, the following pairs can be completed:
1. **f(x) with Graph: A v-shaped acute angled curve joining at (negative 5, negative 1) facing downwards.**
2. **h(x) with Graph: A v-shaped acute angled curve joining at (5, negative 1) facing upwards.**
3. **k(x) with Graph: A v-shaped acute angled curve joining at (5, negative 1) facing downwards.**
4. **g(x) with Graph: A v-shaped acute angled curve joining at (negative 5, positive 1) facing upwards.**
Note: Not all functions will match with the graphs provided in the description as per the equations shared. The functions m(x) and n(x) are not used in the matches above since their descriptions were not part of the graph options provided.