To determine which ordered pairs $(x, y)$ lie on the graph of the exponential function $f(x) = -3 \cdot 2^x + 5$, we need to evaluate $f(x)$ for each given value of $x$ and see if the resulting $y$-value matches the second component of the ordered pair.

Let's break it down:

1. Evaluate the function $f(x) = -3 \cdot 2^x + 5$ for different values of $x$.
2. Compare the result with the given $y$-value in the ordered pair.

Example calculations:

• For $x = 0$: $f(0) = -3 \cdot 2^0 + 5 = -3 \cdot 1 + 5 = -3 + 5 = 2$ So, the ordered pair $(0, 2)$ lies on the graph.

• For $x = 1$: $f(1) = -3 \cdot 2^1 + 5 = -3 \cdot 2 + 5 = -6 + 5 = -1$ So, the ordered pair $(1, -1)$ lies on the graph.

• For $x = 2$: $f(2) = -3 \cdot 2^2 + 5 = -3 \cdot 4 + 5 = -12 + 5 = -7$ So, the ordered pair $(2, -7)$ lies on the graph.

Summary

• The correct ordered pairs that lie on the graph of $f(x) = -3 \cdot 2^x + 5$ are:
  • $(0, 2)$
  • $(1, -1)$
  • $(2, -7)$

If you have any specific ordered pairs you want to check, let me know!

---

Here are 8 related questions you might find helpful:

1. How do you determine if a point lies on the graph of a function?
2. What is the effect of different coefficients in exponential functions?
3. How does changing the base of the exponent affect the graph?
4. What are some real-life applications of exponential functions?
5. How do you graph an exponential function by hand?
6. What does the graph of an exponential decay function look like?
7. How do you find the intercepts of an exponential function?
8. How can transformations (shifts, stretches) be applied to exponential functions?

Tip: For exponential functions, understanding the role of each component (base, coefficient, constant) can help you quickly analyze the graph's behavior.