Sullivan, 8th ed. MAC1140/MAC11476-3: Exponential FunctionsExponential function is a function in the form f(x) = ax where a is a positive real number and a 1. The domain of f is the set of all real numbers. The laws of exponents for real (irrational)exponents are the same as those for integer and rational exponents. Irrational exponents aretruncated to a finite number of digits, so that ar ax. The number e is the number that 11FHGIKJnnapproaches as n. For an exponential function f(x) = ax, a > 0, a ≠ 1, if x is a real number,then ( )( )f xaf x+=1, the base.f(x) = axRange x-intercept y-intercept HorizontalasymptoteCharac-teristicPassesthrougha > 1 [0, ) None (0, 1) x-axis as x -Increasing,one-to-one(0, 1) (1, a)0 < a < 1 [0, ) None (0, 1) x-axis as x  Decreasingone-to-one(0, 1) (1, a)Approximate to three decimal places:1.352. 2eDetermine whether the given function is exponential or not:3. 4.x f(x)x f(x)-1 3-12/30 60 11 913/22 1229/43 15327/8Graph the following exponential functions; state the domain, range, and any horizontal asymptote:3. y = 2x4. y = 12FHGIKJx = 2-x5. y = ex y = 2x – 2 y = 2-x + 3 + 2 = 2-(x – 3)y = 2 - exExponential Equations: If au = av, then u = v.Sullivan, 8th ed. MAC1140/MAC11479.1 2155x10.1142x   11. 24 12xxe e e Suppose the f(x) = 8x12. What is f(5)? When x = 5, what is the point on the graph of f?13. When f(x) = 1/512, what is x, and what is the point on the graph of f?14. If 11x = 7, what does 11-3x equal?15. Determine the exponential function whose graph is given:a. b.Since f(2) = 1, f(x) is shifted 2 units to The horozontal asymptote appears to be y = 3, thus f(x)the right. As f(2 + 1) or f(3) = 6, the is shifted up 3 units. As it is reflected over the x-axis, abase is 6. Thus, f(x) = must be negative. Since f(0) = 2, which is 1 less than thehorizontal asymptote, f(x) has not been shifted horizontally. f(1) = -2; shifting this down 3 units gives us -5. Thus, f(x)