https://file.aiquickdraw.com/mathbot/file/1726659544956201m92jb.jpg

Let's analyze and resolve each question one by one from the image you uploaded:

### 7) Indicar si las siguientes relaciones son o no funciones y justificar la respuesta.

A function assigns exactly one output for each input. Let's check each table:
- **a)** Every \(x\) maps to a unique \(y\). **Function**
- **b)** \(x=2\) maps to \(7\) and \(3\). **Not a function**
- **c)** Every \(x\) maps to a unique \(y\). **Function**
- **d)** \(x=4\) maps to \(9\) and \(5\). **Not a function**
- **e)** Every \(x\) maps to a unique \(y\). **Function**

### 8) Indicar si los siguientes gráficos representan funciones.

A graph represents a function if any vertical line drawn through the graph intersects it at no more than one point (Vertical Line Test).
- **a)** The vertical line intersects at multiple points. **Not a function**
- **b)** The vertical line intersects at only one point everywhere. **Function**

### 9) Indicar si los siguientes gráficos corresponden o no a funciones y justificar la respuesta.

Using the Vertical Line Test:
- **a)** The vertical line intersects at only one point everywhere. **Function**
- **b)** The vertical line intersects at only one point everywhere. **Function**
- **c)** The vertical line intersects at multiple points. **Not a function**
- **d)** The vertical line intersects at only one point everywhere. **Function**

### 10) Observar el gráfico de la función y responder.

- **a) \(f(3)\):** The value at \(x=3\) is approximately \(-1\).
- **b) f^{-1}(3):** No \(y\) value of \(3\) exists on the graph. **Undefined**
- **c) f^{-1}(2):** The pre-image of \(2\) is \(x=1\).
- **d) f^{-1}(4):** No \(y\) value of \(4\) exists on the graph. **Undefined**
- **e) f(x)=0:** At \(x=0\) and \(x=3\), \(f(x)=0\).
- **f) (x,y)=(0,0):** At \(x=0\), \(y\) is \(0\).
- **g) Same image \(f(x)=-1:\)** At

The image contains a set of mathematical problems related to functions and graphs. The user is asked to determine whether various relations and graphs represent functions, applying the Vertical Line Test and analyzing mappings.

In this problem set, we explore relations and their graphical representations to determine if they qualify as functions. Using the Vertical Line Test and analyzing mappings between variables, these exercises are suitable for students in Grades 8-10. The tasks involve identifying correct mappings and applying key function tests.

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