Answer:
the equation has no solution
Answer:
g(x) = - x² - 4 ⇒ A
Step-by-step explanation:
Let us revise the reflection and translation of a function
- If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
- If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)
- If the function f(x) translated horizontally to the right by h units, then its image is g(x) = f(x - h)
- If the function f(x) translated horizontally to the left by h units, then its image is g(x) = f(x + h)
- If the function f(x) translated vertically up by k units, then its image is g(x) = f(x) + k
- If the function f(x) translated vertically down by k units, then its image is g(x) = f(x) – k
f(x) = x² is the blue curve
g(x) is its image is the red curve
∵ g(x) is the image of f(x)
∵ f(x) is opened upward
∵ g(x) is opened downward
→ That means the sign of y-coordinates of all points on the blue
graph are opposite
∴ f(x) is reflected about the x-axis
∴ Its image is - f(x)
∵ The vertex of f(x) is (0, 0)
∵ The vertex of g(x) = (0, -4)
→ That means the function translated 4 units down
∴ - f(x) is translated 4 units down
∴ Its image is - f(x) - 4
∴ g(x) = - f(x) - 4
∵ f(x) = x²
∴ g(x) = - x² - 4
Answer:
<em>h=12, w=24, t=8</em>
Step-by-step explanation:
<u>System of Linear Equations
</u>
We have 3 unknown variables and 3 conditions between them. They form a set of 3 equations with 3 variables.
We have the following data, being
w = price of a sweatshirt
t = price of a T-shirt
h = price of a pair of shorts
19.
The first condition states the price of a sweatshirt is twice the price of a pair of shorts. We can write it as
The second condition states the price of a T-shirt is $4 less than the price of a pair of shorts. We can write it as
The final condition states Brad purchased 3 sweatshirts, 2 pairs of shorts, and 5 T-shirts for $136, thus
This is the system of equations we need to solve for w,t,h
20.
To solve the system, we replace w in terms of h and t in terms of h. Those relations have been already written, so
Operating
Solving for h
The other two variables are
Answer:
a. -3 < x ≤ 5
b. -3 ≤ y < 3
c. (0, 0)
d. x = -3, x = 1, x = 5
e. -3 < x ≤ - 1, and 1 ≤ x ≤ 3,
f. (-1, -1), and (3, -3)
Step-by-step explanation:
a. The domain of a function is the set of the possible independent variable values which is -3 < x ≤ 5
b. The range of a function is the set of the possible values of the dependent variable which is -3 ≤ y < 3
c. The y-intercept is the point the graph crosses the y-axis
The y-intercept in the graph is the point (0, 0)
d. f(x) ≥ 0 when x = -3, x = 1, x = 5
f(x) ≥ 0 over the following range; -3 < x ≤ - 1.5, 0 ≤ x ≤ 1.5, 4.5 ≤ x ≤ 5
e. The intervals over which f(x) is decreasing are;
-3 < x ≤ - 1, and 1 ≤ x ≤ 3,
f. The local minimums where f(x) has the minimum values are;
(-1, -1), and (3, -3)
Answer:
its 1.25
Step-by-step explanation:
