Functions

Exponential functions

*Adapted from DBE Nov 2015 Grade 11, P1, Q5*
Maths formulas

Given:

g(x)=−2(2−x)−2g(x)=−2(2−x)−2

Determine the coordinates of the yy-intercept of gg.

**INSTRUCTION:** Enter your answer as a coordinate, with the values inside brackets and separated by a semicolon e.g. **(x; y)**.

**Answer:**Coordinates of yy-intercept:

To determine the coordinates of the \( y \)-intercept of the function \( g(x) = -2(2^{-x}) - 2 \), we need to evaluate the function when \( x = 0 \). The \( y \)-intercept occurs where the graph crosses the \( y \)-axis, which corresponds to \( x = 0 \).

Substitute \( x = 0 \) into the function:

\[
g(0) = -2(2^{-0}) - 2
\]

Since \( 2^{-0} = 2^0 = 1 \), the equation simplifies to:

\[
g(0) = -2(1) - 2 = -2 - 2 = -4
\]

Thus, the coordinates of the \( y \)-intercept are:

\[
\text{Coordinates of } y\text{-intercept: } (0; -4)
\]

Would you like more details, or do you have any questions?

Here are 5 related questions:
1. How would you find the \( x \)-intercept of the function \( g(x) \)?
2. What does the \( y \)-intercept represent in the context of the graph of \( g(x) \)?
3. How would the \( y \)-intercept change if the function were \( g(x) = -2(2^{-x}) + 3 \)?
4. How can you verify the \( y \)-intercept graphically using a plot of \( g(x) \)?
5. What is the effect of the negative sign in front of the exponential term on the graph of \( g(x) \)?

**Tip:** When calculating intercepts, substitute either \( x = 0 \) for the \( y \)-intercept or \( y = 0 \) for the \( x \)-intercept and solve the resulting equation.

Learn how to determine the coordinates of the y-intercept of the exponential function g(x) = -2(2^{-x}) - 2 with step-by-step solution. This problem involves evaluating the function at x = 0 to find where it crosses the y-axis. Suitable for Grade 11 students studying exponential functions.

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