To answer your questions, we'll need specific forms or equations for the functions \( B(x) \), \( M(x) \), and \( S(x) \). Typically, functions are classified based on their general form:
- **Linear functions**: \( f(x) = mx + b \), where \( m \) and \( b \) are constants.
- **Quadratic functions**: \( f(x) = ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants.
- **Exponential functions**: \( f(x) = a \cdot b^x \), where \( a \) and \( b \) are constants, and \( b > 0 \).
### 1. What type of function is \( B(x) \)?
Without the specific equation for \( B(x) \), we can't definitively classify it. However, here are some ways to determine the type of function based on its properties:
- **Linear**: The graph is a straight line, and the rate of change (slope) is constant.
- **Quadratic**: The graph is a parabola, and the rate of change varies linearly.
- **Exponential**: The graph shows rapid growth or decay, and the rate of change is proportional to the value of the function itself.
### 2. What type of function is \( M(x) \)?
Similar to \( B(x) \), we'd need the equation or specific details about \( M(x) \).
### 3. Transformations of \( M(x) \) with \( k = -10 \):
For a given function \( M(x) \):
- **\( M(x) - 10 \)**: This transformation shifts the graph downward by 10 units.
- **\( M(x - 10) \)**: This transformation shifts the graph to the right by 10 units.
- **\(-10M(x) \)**: This transformation reflects the graph over the x-axis and then stretches it vertically by a factor of 10.
- **\( M(-10x) \)**: This transformation reflects the graph over the y-axis and compresses it horizontally by a factor of 10.
### 4. What type of function is \( S(x) \)?
Again, we need the specific form of \( S(x) \) to classify it. The same methods as for \( B(x) \) apply here.
### 5. Function comparison for \( W(x) \):
To compare \( W(x) \) with \( B(x) \), \( M(x) \), and \( S(x) \), we need to know the form of \( W(x) \). If \( W(x) \) is given as linear, quadratic, or exponential, we can match it with the type of \( B(x) \), \( M(x) \), or \( S(x) \) that has the same form.
To provide a specific classification and detailed transformations, please share the equations or specific properties of the functions \( B(x) \), \( M(x) \), \( S(x) \), and \( W(x) \).
