Let's analyze the function given:
[tex]\[ a(x) = 8x + 1 \][/tex]
### Step-by-Step Solution:
1. Identify the Type of Function:
- A linear function can be written in the form [tex]\( y = mx + b \)[/tex], where [tex]\( m \)[/tex] is the slope and [tex]\( b \)[/tex] is the y-intercept.
- An exponential function is generally in the form [tex]\( y = a \cdot b^x \)[/tex], where [tex]\( a \)[/tex] is a constant and [tex]\( b \)[/tex] is the base of the exponential term.
- A quadratic function is in the form [tex]\( y = ax^2 + bx + c \)[/tex], where [tex]\( a \)[/tex], [tex]\( b \)[/tex], and [tex]\( c \)[/tex] are constants and the term [tex]\( ax^2 \)[/tex] indicates the quadratic nature due to the [tex]\( x^2 \)[/tex] term.
2. Compare with the Linear Form:
- The given function [tex]\( a(x) = 8x + 1 \)[/tex] closely matches the linear form [tex]\( y = mx + b \)[/tex]. Here, [tex]\( m = 8 \)[/tex] (slope) and [tex]\( b = 1 \)[/tex] (y-intercept).
3. Conclusion:
- Since the function [tex]\( a(x) = 8x + 1 \)[/tex] fits the structure of a linear function (where the highest power of [tex]\( x \)[/tex] is 1), we can confidently classify it as a linear function.
Thus, the given function [tex]\( a(x) = 8x + 1 \)[/tex] is Linear.
