Question

for each function below, choose the correct description of its graph. (a) choose the description for ( h(x) = 4x^2 + 2x ). vertical line horizontal line parabola opening downward parabola opening upward line with a negative slope line with a positive slope (b) choose the description for ( k(x) = 3 ). vertical line horizontal line parabola opening downward parabola opening upward line with a negative slope line with a positive slope (c) choose the description for ( g(x) = x - 1 ). vertical line horizontal line parabola opening downward parabola opening upward line with a negative slope line with a positive slope

Explanation:

Part (a)

Step1: Identify function type

The function \( h(x) = 4x^2 + 2x \) is a quadratic function (degree 2), so its graph is a parabola.

Step2: Determine parabola direction

For a quadratic \( ax^2+bx+c \), if \( a>0 \), it opens upward. Here \( a = 4>0 \), so it opens upward.

Step1: Identify function type

The function \( k(x)=3 \) is a constant function. A constant function \( y = c \) (where \( c \) is constant) has a horizontal line graph (since \( y \) - value is same for all \( x \)).

Step2: Confirm line type

A horizontal line has a slope of 0, and \( k(x)=3 \) is \( y = 3 \), which is a horizontal line.

Step1: Identify function type

The function \( g(x)=x - 1 \) is a linear function in the form \( y=mx + b \) (here \( m = 1 \), \( b=-1 \)).

Step2: Determine slope sign

The slope \( m = 1>0 \), so it's a line with a positive slope.

Answer:

parabola opening upward

Part (b)