Alright, let's break this down step by step by evaluating and simplifying each of the given functions:
### Given Functions:
1. [tex]\( f(x) = 8x \)[/tex]
2. [tex]\( g(x) = 2x - 2 \)[/tex]
3. [tex]\( h(x) = -6x^2 + 14x - 8 \)[/tex]
### Simplified Expressions:
Let's determine each function based on the information provided:
#### 1. [tex]\( f(x) = 8x \)[/tex]
This is a linear function where the coefficient of [tex]\( x \)[/tex] is 8, meaning that for any input [tex]\( x \)[/tex], the output is just 8 times [tex]\( x \)[/tex].
#### 2. [tex]\( g(x) = 2x - 2 \)[/tex]
This is another linear function in standard form [tex]\( g(x) = mx + b \)[/tex], where the coefficient of [tex]\( x \)[/tex] (slope) is 2 and the y-intercept is -2.
#### 3. [tex]\( h(x) = -6x^2 + 14x - 8 \)[/tex]
This is a quadratic function in the standard form [tex]\( h(x) = ax^2 + bx + c \)[/tex] where:
- The coefficient [tex]\( a = -6 \)[/tex]
- The coefficient [tex]\( b = 14 \)[/tex]
- The constant term [tex]\( c = -8 \)[/tex]
These expressions are already simplified and written in descending order of powers of [tex]\( x \)[/tex].
### Summary of Simplified Expressions:
1. [tex]\( f(x) = 8x \)[/tex]
2. [tex]\( g(x) = 2x - 2 \)[/tex]
3. [tex]\( h(x) = -6x^2 + 14x - 8 \)[/tex]
These are the simplest forms of the given functions:
- For [tex]\( f(x) \)[/tex], it is simply [tex]\( 8x \)[/tex].
- For [tex]\( g(x) \)[/tex], it is [tex]\( 2x - 2 \)[/tex].
- For [tex]\( h(x) \)[/tex], it is [tex]\( -6x^2 + 14x - 8 \)[/tex].
I hope this detailed explanation clarifies how to interpret and simplify these functions!
