1. Correct answer for linear function passing through given points: The zero of \(k\) is -7. 2. Correct answer for graph of \(y = 16(0.5)^x\): The x-intercept is (0.5, 0). 3. The horizontal asymp

Let's address each question one by one. **Question 1:** The linear function \( k \) passes through the points \((-7, 0)\) and \((1, 8)\). First, determine the slope (\(m\)). The slope formula is: \[ m = \frac{y_2 - y_1}{x_2 - x_1} \] Using the given points \((-7, 0)\) and \((1, 8)\): \[ m = \frac{8 - 0}{1 - (-7)} = \frac{8}{8} = 1 \] Now, any linear function passing through the x-intercept \((-7, 0)\) must have \(-7\) as its zero. So, the correct statement is: B. The zero of \( k \) is \(-7\). **Question 2:** Consider the function \( y = 16(0.5)^x \). - Option A: The x-intercept is \((0.5, 0)\). **Not true.** The x-intercept is found when \( y = 0 \), which doesn't occur for this exponential function. - Option B: The graph has a horizontal asymptote at \( y = 0 \). **True.** Exponential functions of the form \( y = a(b)^x \) with \( 0 < b < 1 \) have a horizontal asymptote at \( y = 0 \). - Option C: The graph is decreasing for all values of \( x \). **True.** Since \( 0 < b < 1 \), the function decreases. - Option D: The y-intercept is \((0, 16)\). **True.** When \( x=0 \), \( y = 16(0.5)^0 = 16 \). So, the correct answer is: A. The x-intercept is \((0.5, 0)\). **Question 3:** For the function \( y = 16(0.75)^x \), the horizontal asymptote is: When \( x \) approaches a large positive number, \( (0.75)^x \) approaches 0. Therefore, the horizontal asymptote is: \[ y = 0 \] **Question 4:** Given the function \( A(t) = 1,550(1.02)^t \): The correct interpretation: - The initial deposit was \$1,550 (the coefficient before the exponential part). - The amount increases by 2% each year (since 1.02 represents a 2% increase). Thus, the correct interpretation is: D. The initial deposit in the investment account was \$1,550. **Question 7:** Divide \( x^2 + 7x + 12 \) by \( x + 4 \). Using polynomial long division or synthetic division: \[ x^2 + 7x + 12 \div (x + 4) \] 1. \( x^2 \div x = x \) 2. Multiply \( x \) by \( x + 4 \): \( x(x + 4) = x^2 + 4x \) 3. Subtract: \[ (x^2 + 7x + 12) - (x^2 + 4x) = 3x + 12 \] 4. Divide \( 3x \div x = 3 \) 5. Multiply \( 3 \) by \( x + 4 \): \( 3(x + 4) = 3x + 12 \) 6. Subtract: \[ (3x + 12) - (3x + 12) = 0 \] The quotient is: A. \( x + 3 \) So, the correct answer is: D. x + 3