Determine if each function is increasing or decreasing 7. $$ f(x)=4 x+3 $$ $$ \begin{array}{ll} ext { 9. } a(x)=5-2 x & ext { 8. } g(x)=5 x+6 \ ext { 11. } h(x)=-2 x+4 & ext { 10. } b(x)=8-3 x \ ext { 13. } j(x)=\frac{1}{2} x-3 & ext { 12. } k(x)=-4 x+1 \ ext { 15. } n(x)=-\frac{1}{3} x-2 & ext { 14. } p(x)=\frac{1}{4} x-5\end{array} $$

Question

Determine if each function is increasing or decreasing 7. $$ f(x)=4 x+3 $$ $$ \begin{array}{ll}	ext { 9. } a(x)=5-2 x & 	ext { 8. } g(x)=5 x+6 \ 	ext { 11. } h(x)=-2 x+4 & 	ext { 10. } b(x)=8-3 x \ 	ext { 13. } j(x)=\frac{1}{2} x-3 & 	ext { 12. } k(x)=-4 x+1 \ 	ext { 15. } n(x)=-\frac{1}{3} x-2 & 	ext { 14. } p(x)=\frac{1}{4} x-5\end{array} $$

UpStudy AI · Accepted Answer

To determine whether each function is increasing or decreasing, we can analyze the slope of each linear function. The slope of a linear function in the form $$ f(x) = mx + b $$ is given by the coefficient $$ m $$:

- If $$ m > 0 $$, the function is increasing.
- If $$ m < 0 $$, the function is decreasing.
- If $$ m = 0 $$, the function is constant.

Now, let's analyze each function:

1. **$$ f(x) = 4x + 3 $$**: The slope $$ m = 4 $$ (increasing).
2. **$$ g(x) = 5x + 6 $$**: The slope $$ m = 5 $$ (increasing).
3. **$$ a(x) = 5 - 2x $$**: The slope $$ m = -2 $$ (decreasing).
4. **$$ h(x) = -2x + 4 $$**: The slope $$ m = -2 $$ (decreasing).
5. **$$ b(x) = 8 - 3x $$**: The slope $$ m = -3 $$ (decreasing).
6. **$$ j(x) = \frac{1}{2}x - 3 $$**: The slope $$ m = \frac{1}{2} $$ (increasing).
7. **$$ k(x) = -4x + 1 $$**: The slope $$ m = -4 $$ (decreasing).
8. **$$ n(x) = -\frac{1}{3}x - 2 $$**: The slope $$ m = -\frac{1}{3} $$ (decreasing).
9. **$$ p(x) = \frac{1}{4}x - 5 $$**: The slope $$ m = \frac{1}{4} $$ (increasing).

### Summary:
- **Increasing Functions**: $$ f(x) $$, $$ g(x) $$, $$ j(x) $$, $$ p(x) $$
- **Decreasing Functions**: $$ a(x) $$, $$ h(x) $$, $$ b(x) $$, $$ k(x) $$, $$ n(x) $$
- **Increasing Functions**: $$ f(x) = 4x + 3 $$, $$ g(x) = 5x + 6 $$, $$ j(x) = \frac{1}{2}x - 3 $$, $$ p(x) = \frac{1}{4}x - 5 $$ - **Decreasing Functions**: $$ a(x) = 5 - 2x $$, $$ h(x) = -2x + 4 $$, $$ b(x) = 8 - 3x $$, $$ k(x) = -4x + 1 $$, $$ n(x) = -\frac{1}{3}x - 2 $$

Determine if each function is increasing or decreasing
7.

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