Question

for each function below, choose the correct description of its graph. (a) choose the description for f(x) = -x² - 3x + 1. vertical line horizontal line line with a negative slope line with a positive slope parabola opening downward parabola opening upward (b) choose the description for g(x) = -x + 4. vertical line horizontal line line with a negative slope line with a positive slope parabola opening downward parabola opening upward (c) choose the description for k(x) = 1. vertical line horizontal line line with a negative slope line with a positive slope parabola opening downward parabola opening upward

Explanation:

Part (a)

Step1: Identify function type

The function \( f(x) = -x^2 - 3x + 1 \) is a quadratic function (degree 2), so its graph is a parabola.

Step2: Determine parabola direction

For a quadratic function \( ax^2+bx+c \), if \( a < 0 \), the parabola opens downward. Here, \( a=-1 < 0 \), so it opens downward.

Step1: Identify function type

The function \( g(x)=-x + 4 \) is a linear function (degree 1), so its graph is a line.

Step2: Determine slope sign

In slope - intercept form \( y = mx + b \), the slope \( m=-1 \), which is negative. So it is a line with a negative slope.

Step1: Analyze the function \( k(x) = 1 \)

The function \( k(x)=1 \) can be written as \( y = 1 \), which is a horizontal line (since for all \( x \), \( y \) is constant).

Answer:

parabola opening downward

Part (b)