Question

Choose the correct formula for the function h.

a) h(x) = -3x - 2 - 1
b) h(x) = -3x - 2
c) h(x) = -3x 2 - 1
d) h(x) = -3x 2 1

Answer 1

The correct formula for the function
`\( h \) is b) \( h(x) = -3x - 2 \).`

Explanation:

In the given options, the correct formula is identified by analyzing the structure and coefficients of the function. The correct formula follows the general form
`\( h(x) = mx + b \)` where
`\( m \)` is the slope (coefficient of x and b is the y-intercept (constant term).

Let's break down each option:

a)
`\( h(x) = -3x - 2 - 1 \)`: This option has an additional constant term (-1) which is not present in the standard form.

b)
`\( h(x) = -3x - 2 \):` This option matches the standard form with a slope of -3 and a y-intercept of -2.

c)
`\( h(x) = -3x^2 - 1 \)`: This option includes a squared term
`(\( x^2 \))`, indicating a quadratic function, whereas we are looking for a linear function.

d)
`\( h(x) = -3x^2 + 1 \):` Similar to option c, this is a quadratic function with a squared term.

By comparing the options with the standard form of a linear function,
`\( h(x) = mx + b \)` option b is the correct formula for the given function h . It has the appropriate coefficients for a linear equation, making it the accurate representation of the function.