Question

question
find $g(-3)$.
$g(x)$
$h(x) = 2x^2 + 5x - 2$

Explanation:

Step1: Determine the type of function \( g(x) \)

The graph of \( g(x) \) is a straight line, so \( g(x) \) is a linear function. Let's find its equation. First, find the slope \( m \). We can see two points on the line, for example, when \( x = 0 \), \( y = 5 \) (y - intercept), and when \( x=-5 \), \( y = 0 \) (x - intercept). The slope \( m=\frac{y_2 - y_1}{x_2 - x_1}=\frac{5 - 0}{0-(-5)} = 1 \). So the equation of the line is \( g(x)=x + 5 \) (using slope - intercept form \( y=mx + b \), where \( m = 1 \) and \( b = 5 \)).

Step2: Substitute \( x=-3 \) into \( g(x) \)

Now we substitute \( x=-3 \) into \( g(x)=x + 5 \). So \( g(-3)=-3 + 5 \).

Step3: Calculate the result

\( -3+5 = 2 \).

Answer:

\( 2 \)