Question

For each function below, choose the correct description of its graph.

line
vertical horizontal a line
line with line
slope
with a negative positive slope
parabola opening down
parabola opening up

F(x)=x-1

K(x)=3x^2+4x-2

g(x)=-4

Answer 1

Let's analyze each function one by one to determine the correct description of its graph:

1. **F(x) = x - 1**

This is a linear function of the form \(y = mx + b\) where \(m = 1\) (the coefficient of \(x\)) and \(b = -1\) (the y-intercept). Since the slope is positive, the graph of this function is a line with a **positive slope**.

2. **K(x) = 3x^2 + 4x - 2**

This is a quadratic function of the form \(y = ax^2 + bx + c\) where \(a = 3\), \(b = 4\), and \(c = -2\). Since \(a\) is positive (3 > 0), the parabola opens **up**.

3. **g(x) = -4**

This is a constant function where the output is always -4, regardless of the input \(x\). The graph of this function is a straight horizontal line where \(y = -4\).

Now, summarizing:

- **F(x) = x - 1**: **line with positive slope**
- **K(x) = 3x^2 + 4x - 2**: **parabola opening up**
- **g(x) = -4**: **horizontal line**