A function $$ f(x) $$ is a linear function and the function $$ g(x)=f(x)+k $$ .If the value of k is 4 , how does the graph of $$ g(x) $$ compare with the graph $$ f(x) $$ ?

Question

UpStudy AI · Accepted Answer

When dealing with linear functions, any modification involving the addition of a constant affects the graph in a specific way.

Given:
- **$$ f(x) $$** is a linear function. Its graph is a straight line.
- **$$ g(x) = f(x) + k $$**, where $$ k = 4 $$.

**Impact of Adding $$ k $$:**
- Adding a constant $$ k $$ to $$ f(x) $$ results in a vertical shift of the graph.
- Specifically, $$ g(x) = f(x) + 4 $$ shifts the entire graph of $$ f(x) $$ **upward** by 4 units.

**Characteristics of the Transformation:**
- **Slope**: The slope of $$ f(x) $$ and $$ g(x) $$ remains the same since the addition of a constant does not affect it.
- **Y-Intercept**: The y-intercept of $$ g(x) $$ is 4 units higher than that of $$ f(x) $$.

**Conclusion:**
The graph of $$ g(x) $$ will be a straight line that is **parallel** to the graph of $$ f(x) $$, positioned **4 units above** it.

**Visual Representation:**

---

**Summary:** Adding 4 to the linear function $$ f(x) $$ shifts its graph upward by 4 units, resulting in a parallel line for $$ g(x) $$.

**Answer:** Its graph is the same straight line shifted upward by four units, running parallel to f (x ).
The graph of $$ g(x) $$ is the same straight line as $$ f(x) $$ but shifted upward by 4 units.

A function is a linear function and the function
.If the value of k is 4 , how does the graph of compare with the
graph ?

Solución de inteligencia artificial de Upstudy

Responder

Solución

Bonus Knowledge

preguntas relacionadas

Latest Algebra Questions

A function is a linear function and the function .If the value of k is 4 , how does the graph of compare with the graph ?