In Exercises 1-3, \( d \) function. Explain. 1. \( y=9 x \)

To analyze the function \( y = 9x \), we can follow these steps: 1. **Identify the type of function**: The equation \( y = 9x \) is a linear function. Linear functions are characterized by their constant rate of change, which means that for every unit increase in \( x \), \( y \) increases by a constant amount. 2. **Determine the slope and y-intercept**: - The slope \( m \) of the function is the coefficient of \( x \), which is \( 9 \). This means that for every increase of \( 1 \) in \( x \), \( y \) increases by \( 9 \). - The y-intercept \( b \) is the constant term in the equation. Since there is no constant term in this equation, the y-intercept is \( 0 \). This means the line passes through the origin (0,0). 3. **Graph the function**: To graph the function, we can plot the y-intercept and use the slope to find another point. Starting at the origin (0,0): - From (0,0), move up \( 9 \) units and \( 1 \) unit to the right to reach the point (1,9). - Draw a straight line through these points, extending in both directions. 4. **Behavior of the function**: - As \( x \) increases, \( y \) increases linearly without bound. - As \( x \) decreases, \( y \) also decreases linearly without bound. 5. **Domain and Range**: - The domain of the function is all real numbers \( (-\infty, \infty) \) since \( x \) can take any value. - The range is also all real numbers \( (-\infty, \infty) \) since \( y \) can take any value depending on \( x \). In summary, the function \( y = 9x \) is a linear function with a slope of \( 9 \) and a y-intercept of \( 0 \). It increases linearly as \( x \) increases and has a domain and range of all real numbers.